R. Aghajani, P. Robert, and W. Sun, A large scale analysis of unreliable stochastic networks, Ann. Appl. Probab, vol.28, issue.2, pp.851-887, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01359208

M. Alanyali and M. Dashouk, On power-of-choice in downlink transmission scheduling, 2008 Information Theory and Applications Workshop, pp.12-17, 2008.

D. Aldous, Probability approximations via the Poisson clumping heuristic, 1989.

D. Aldous and P. Diaconis, Strong uniform times and finite random walks, Advances in Applied Mathematics, vol.8, pp.69-97, 1987.

D. J. Aldous, Deterministic and stochastic models for coalescence (aggregation and coagulation): A review of the mean-field theory for probabilists, Bernoulli, vol.5, pp.3-48, 1999.

A. Alfonsi, J. Corbetta, J. , and B. , Evolution of the wasserstein distance between the marginals of two Markov processes, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01390887

D. Alistarh, J. Kopinsky, J. Li, and G. Nadiradze, The power of choice in priority scheduling, Proceedings of the ACM Symposium on Principles of Distributed Computing, pp.283-292, 2017.

D. F. Anderson and T. G. Kurtz, Continuous time Markov chain models for chemical reaction networks, Design and Analysis of Biomolecular Circuits, pp.3-42, 2011.

R. F. Anderson and S. Orey, Small random perturbation of dynamical systems with reflecting boundary, Nagoya Math. J, vol.60, pp.189-216, 1976.

L. Andreis, P. D. Pra, and M. Fischer, Mckean-vlasov limit for interacting systems with simultaneous jumps

J. M. Andrews and C. J. Roberts, A Lumry-Eyring nucleated polymerization model of protein aggregation kinetics: 1. Aggregation with pre-equilibrated unfolding, J Phys Chem B, vol.111, pp.7897-7913, 2007.

V. I. Arnold and I. Systems, Encyclopaedia of Mathematical Sciences book series, 1988.

K. B. Athreya and P. E. Ney, Die Grundlehren der mathematischen Wissenschaften, 0196.

Y. Azar, A. Z. Broder, A. R. Karlin, and E. Upfal, Balanced allocations, SIAM journal on computing, vol.29, pp.180-200, 1999.

J. M. Ball, J. Carr, and O. Penrose, The Becker-Döring cluster equations: Basic properties and asymptotic behaviour of solutions, Comm. Math. Phys, vol.104, issue.4, pp.657-692, 1986.

R. Becker and W. Döring, Kinetische behandlung der keimbildung in übersättigten dämpfen, Annalen der Physik, vol.416, pp.719-752, 1935.

J. Bertoin, Random fragmentation and coagulation processes, of Cambridge Studies in Advanced Mathematics, vol.102, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00103015

J. Bertoin, Markovian growth-fragmentation processes, Bernoulli, vol.23, pp.1082-1101, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01152370

P. Billingsley, Convergence of probability measures, INC, pp.1-287, 2009.

N. H. Bingham, Fluctuation theory for the Ehrenfest urn, Advances in Applied Probability, vol.23, pp.598-611, 1991.

D. Borthakur, HADOOP APACHE, 2008.

P. Bozaykut, N. K. Ozer, and B. Karademir, Regulation of protein turnover by heat shock proteins. Free Radic, Biol. Med, vol.77, pp.195-209, 2014.

M. Bramson, Y. Lu, and B. Prabhakar, Decay of tails at equilibrium for fifo join the shortest queue networks, The Annals of Applied Probability, vol.23, pp.1841-1878, 2013.

W. Braun and K. Hepp, The vlasov dynamics and its fluctuations in the 1/n limit of interacting classical particles, Comm. Math. Phys, vol.56, pp.101-113, 1977.

P. Brémaud, Point processes and queues: Martingale dynamics, 1981.

T. Brown, A martingale approach to the Poisson convergence of simple point processes, The Annals of Probability, vol.6, pp.615-628, 1978.

A. Budhiraja and E. Friedlander, Diffusion approximations for load balancing mechanisms in cloud storage systems, 2017.

A. Budhiraja, D. Mukherjee, and R. Wu, Supermarket model on graphs

V. Calvez, M. Doumic, and P. Gabriel, Self-similarity in a general aggregation-fragmentation problem. application to fitness analysis, Journal de Mathématiques Pures et Appliquées, vol.98, pp.1-7, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00539279

P. Caputo, P. Dai-pra, and G. Posta, Convex entropy decay via the Bochner-Bakry-Emery approach, Annales de l'institut Henri Poincaré, vol.45, issue.3, pp.734-753, 2009.

J. A. Carrillo, R. J. Mccann, and C. Villani, Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates, Revista Matemática Iberoamericana, vol.19, pp.971-1018, 2003.

P. Cattiaux, A. Guillin, and F. Malrieu, Probabilistic approach for granular media equations in the non-uniformly convex case, Probability Theory and Related Fields, vol.140, pp.19-40, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00021591

C. C. Chang and H. Yau, Fluctuations of one-dimensional Ginzburg-Landau models in nonequilibrium, Comm. Math. Phys, vol.145, pp.209-234, 1992.

F. Chang, J. Dean, S. Ghemawat, W. C. Hsieh, D. A. Wallach et al., Bigtable: A distributed storage system for structured data, Proceedings of the 7th USENIX Symposium on Operating Systems Design and Implementation, vol.7, pp.15-15, 2006.

H. Chen and A. Mandelbaum, Discrete flow networks: bottleneck analysis and fluid approximations, Mathematics of Operation Research, vol.16, issue.2, pp.408-446, 1991.

B. Chun, F. Dabek, A. Haeberlen, E. Sit, H. Weatherspoon et al., Efficient replica maintenance for distributed storage systems, Proceedings of the 3rd Conference on Networked Systems Design & Implementation -Volume, vol.3, pp.4-4, 2006.

F. Comets, Nucleation for a long range magnetic model, Ann. Inst. H. Poincaré Probab. Statist, vol.23, pp.135-178, 1987.

F. Comets, Lecture notes from the 46th Probability Summer School, Lecture Notes in Mathematics, vol.2175, 2016.

G. Da-prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions. Encyclopedia of Mathematics and its Applications, 1992.

F. Dabek, J. Li, E. Sit, J. Robertson, F. F. Kaashoek et al., Designing a DHT for low latency and high throughput, the 1st Symposium on Networked Systems Design and Implementation, 2004.

J. K. Davis and S. S. Sindi, A study in nucleated polymerization models of protein aggregation, Applied Mathematics Letters, vol.40, pp.97-101, 2015.

D. A. Dawson, Measure-valued Markov processes, École d'Été de Probabilités de Saint-Flour XXI-1991, vol.1541, pp.1-260, 1993.

G. Decandia, D. Hastorun, M. Jampani, G. Kakulapati, A. Lakshman et al., Dynamo: Amazon's highly available key-value store, Proceedings of Twenty-first ACM SIGOPS Symposium on Operating Systems Principles, pp.205-220, 2007.

F. Hollander, Lectures from the 37th Probability Summer School, Lecture Notes in Mathematics, vol.1974, 2007.

J. Deschamps, E. Hingant, Y. , and R. , Boundary value for a nonlinear transport equation emerging from a stochastic coagulation-fragmentation type model, 2014.

L. Desvillettes and C. Villani, On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems: the linear Fokker-Planck equation, Communications on Pure and Applied Mathematics, vol.54, pp.1-42, 2001.

P. Diaconis, Group representations in probability and statistics, Institute of Mathematical Statistics, 1988.

P. Diaconis, R. L. Graham, and J. A. Morrison, Asymptotic analysis of a random walk on a hypercube with many dimensions, Random Structures Algorithms, vol.1, pp.51-72, 1990.

C. Dobson, The generic nature of protein folding and misfolding, Protein Misfolding, Aggregation, and Conformational Diseases, vol.4, pp.21-41, 2006.

C. M. Dobson, Protein folding and misfolding, Nature, vol.426, pp.884-890, 2003.

M. Doumic, S. Eugène, R. , and P. , Asymptotics of stochastic protein assembly models, SIAM Journal on Applied Mathematics, vol.76, pp.2333-2352, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01301266

R. Durrett, B. L. Granovsky, and S. Gueron, The equilibrium behavior of reversible coagulation-fragmentation processes, Journal of Theoretical Probability, vol.12, issue.2, pp.447-474, 1999.

K. Eden, R. Morris, J. Gillam, C. E. Macphee, A. et al., Competition between primary nucleation and autocatalysis in amyloid fibril self-assembly, Biophysical Journal, vol.108, pp.632-643, 2015.

P. Ehrenfest, Uber zwei bekannte einwande gegen das boltzmannsche h theorem, Phys. Z, vol.8, pp.311-314, 1907.

N. El-karoui and M. Chaleyat-maurel, Un problème de réflexion et ses applications au temps local et aux équations différentielles stochastiques sur R, Exposés du Séminaire J. Azéma-M. Yor, pp.1976-1977, 1978.

N. Ercolani, S. Jansen, and D. Ueltschi, Random partitions in statistical mechanics, Electronic Journal of Probability, vol.19, p.pp, 2014.

S. N. Ethier and T. G. Kurtz, Markov processes: Characterization and convergence, 1986.

S. Eugène, W. Xue, P. Robert, and M. Doumic, Insights into the variability of nucleated amyloid polymerization by a minimalistic model of stochastic protein assembly, Journal of Chemical Physics, vol.144, p.175101, 2016.

M. R. Evans and T. Hanney, Nonequilibrium statistical mechanics of the zerorange process and related models, Journal of Physics A: Mathematical and General, vol.38, p.195, 2005.

S. M. Fallat, J. , and C. R. , Totally nonnegative matrices. Princeton Series in Applied Mathematics, 2011.

M. Feuillet, R. , and P. , A scaling analysis of a transient stochastic network, Advances in Applied Probability, vol.46, issue.2, pp.516-535, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00684697

M. Firestone, R. D. Levie, and S. Rangarajan, On one-dimensional nucleation and growth of "living" polymers I. homogeneous nucleation, Journal of Theoretical Biology, vol.104, issue.4, pp.535-552, 1983.

M. Freidlin and A. Wentzell, Random Perturbations of Dynamical Systems. No. v. 260 in Grundlehren der mathematischen Wissenschaften, 1998.

B. Fristedt, The structure of random partitions of large integers, Transactions of the American Mathematical Society, vol.337, pp.703-735, 1993.

A. Ganguly, K. Ramanan, P. Robert, and W. Sun, A Large-Scale network with moving servers, Proc. of Sigmetrics workshop MAMA, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01644146

S. Ghemawat, H. Gobioff, and S. Leung, The Google file system, the 9th symposium on Operating systems principles, pp.29-43, 2003.

J. Gillam and C. Macphee, Modelling amyloid fibril formation kinetics: mechanisms of nucleation and growth, Journal of Physics: Condensed Matter, vol.25, p.373101, 2013.

C. Godrèche, From Urn Models to Zero-Range Processes: Statics and Dynamics, pp.261-294, 2007.

C. Godrèche and J. Luck, Nonequilibrium dynamics of urn models, Journal of Physics: Condensed Matter, vol.14, pp.1601-1615, 2002.

C. Graham, Chaoticity on path space for a queueing network with selection of the shortest queue among several, Journal of Applied Probability, vol.37, pp.198-211, 2000.

C. Graham, Functional central limit theorems for a large network in which customers join the shortest of several queues, Probability Theory and Related Fields, vol.131, issue.1, pp.97-120, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00001392

M. Z. Guo, G. C. Papanicolaou, and S. R. Varadhan, Nonlinear diffusion limit for a system with nearest neighbor interactions, Comm. Math. Phys, vol.118, pp.31-59, 1988.

J. Harrison and M. Reiman, Reflected Brownian motion on an orthant, Annals of Probability, vol.9, pp.302-308, 1981.

A. Heneghan, P. Wilson, and A. Haymet, Heterogeneous nucleation of supercooled water, and the effect of an added catalyst, Proceedings of the National Academy of Sciences, vol.99, pp.9631-9634, 2002.

E. Hingant, R. Yvinec, S. Deterministic, and . Becker, Döring equations: Past and Recent Mathematical Developments, 2016.

R. A. Horn, J. , and C. R. , Matrix analysis, 1990.

P. Hunt and T. Kurtz, Large loss networks, Stochastic Processes and their Applications, vol.53, pp.363-378, 1994.

P. Jabin and B. Niethammer, On the rate of convergence to equilibrium in the becker-döring equations, Journal of Differential Equations, vol.191, pp.518-543, 2003.

M. Jacobsen, Point process theory and applications. Probability and its Applications, 2006.

J. Jacod, Calcul stochastique et problèmes de martingales, Lecture Notes in Mathematics, vol.714, 1979.

J. Jacod and A. N. Shiryaev, Limit theorems for stochastic processes, vol.288

. Springer-verlag, , 1987.

M. Jelasity, A. Montresor, G. P. Jesi, and S. Voulgaris, The Peersim simulator

I. Jeon, Existence of gelling solutions for coagulation-fragmentation equations, Comm. Math. Phys, vol.194, issue.3, pp.541-567, 1998.

A. Joulin, A new Poisson-type deviation inequality for Markov jump processes with positive Wasserstein curvature, Bernoulli. Official Journal of the Bernoulli Society for Mathematical Statistics and Probability, vol.15, pp.532-549, 2009.

M. Kac, Foundations of kinetic theory, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, vol.3, pp.171-197, 1956.

S. Karlin and J. Mcgregor, Ehrenfest urn models, Journal of Applied Probability, vol.2, pp.352-376, 1965.

A. Karthik, A. Mukhopadhyay, and R. R. Mazumdar, Choosing among heterogeneous server clouds, Queueing Systems, vol.85, issue.1, pp.1-29, 2017.

Y. Kasahara and S. Watanabe, Limit theorems for point processes and their functionals, Journal of the Mathematical Society of Japan, vol.38, pp.543-574, 1986.

D. Kashchiev, Protein polymerization into fibrils from the viewpoint of nucleation theory, Biophys. J, vol.109, pp.2126-2136, 2015.

D. Kashchiev, Modeling the effect of monomer conformational change on the early stage of protein self-assembly into fibrils, The Journal of Physical Chemistry B, vol.121, pp.35-46, 2017.

J. Keilson, Markov chains Models-Rarity and exponentiality, vol.28, 1979.

F. P. Kelly, Loss networks, Ann. Appl. Probab, vol.1, issue.3, pp.319-378, 1991.

R. Khasminskii, Stochastic stability of differential equations. Mechanics-analysis. Sijthoff & Noordhoff, 1980.

R. Khasminskii and N. Krylov, On averaging principle for diffusion processes with null-recurrent fast component, Stochastic Processes and their applications, vol.93, pp.229-240, 2001.

J. F. Kingman, Poisson processes. Oxford studies in probability, 1993.

V. F. Kolchin, B. A. Sevastyanov, and C. , , 1978.

T. Kurtz, Averaging for martingale problems and stochastic approximation, Control and Information sciences, vol.177, pp.186-209, 1992.

T. G. Kurtz, The relationship between stochastic and deterministic models for chemical reactions, The Journal of Chemical Physics, vol.57, pp.2976-2978, 1972.

T. G. Kurtz, Strong approximation theorems for density dependent markov chains, Stochastic Processes and their Applications, vol.6, pp.223-240, 1978.

A. Lakshman, P. Malik, and . Cassandra, A decentralized structured storage system, SIGOPS Oper. Syst. Rev, vol.44, pp.35-40, 2010.

G. Last and A. Brandt, Marked point processes on the real line, Probability and its Applications, 1995.

P. Laurençot and S. Mischler, From the becker-döring to the lifshitz-slyozovwagner equations, Journal of Statistical Physics, vol.106, pp.957-991, 2002.

S. Legtchenko, S. Monnet, P. Sens, and G. Muller, RelaxDHT: A churnresilient replication strategy for peer-to-peer distributed hash-tables, ACM Trans. Auton. Adapt. Syst, vol.7, issue.2, p.18, 2012.

E. Luçon and W. Stannat, Mean field limit for disordered diffusions with singular interactions, The Annals of Applied Probability, vol.24, pp.1946-1993, 2014.

M. J. Luczak and C. Mcdiarmid, Asymptotic distributions and chaos for the supermarket model, Electronic Journal of Probability, vol.12, issue.3, pp.75-99, 2007.

S. T. Maguluri, R. Srikant, Y. , and L. , Stochastic models of load balancing and scheduling in cloud computing clusters, 2012 Proceedings IEEE INFOCOM, pp.702-710, 2012.

P. A. Markowich and C. Villani, On the trend to equilibrium for the Fokker-Planck equation: an interplay between physics and functional analysis, VI Workshop on Partial Differential Equations, Part II, vol.19, pp.1-29, 1999.

H. P. Mckean, Propagation of chaos for a class of non-linear parabolic equations, Stochastic Differential Equations (Lecture Series in Differential Equations, Session 7, pp.41-57, 1967.

J. J. Mcmanus, P. Charbonneau, E. Zaccarelli, A. , and N. , The physics of protein self-assembly, 2016.

S. Meyn and R. Tweedie, Markov chains and stochastic stability. Communications and control engineering series, 1993.

M. Mitzenmacher, A. W. Richa, and R. Sitaraman, The power of two random choices: A survey of techniques and results, Handbook of Randomized Computing, pp.255-312, 2000.

H. Mohamed, R. , and P. , A probabilistic analysis of some tree algorithms, Annals of Applied Probability, vol.15, pp.2445-2471, 2005.
URL : https://hal.archives-ouvertes.fr/inria-00070586

A. Montresor, J. , and M. , PeerSim: A scalable P2P simulator, Proc. of the 9th Int. Conference on Peer-to-Peer (P2P'09), pp.99-100, 2009.

A. M. Morris, M. A. Watzky, and R. G. Finke, Protein aggregation kinetics, mechanism, and curve-fitting: a review of the literature, Biochimica et Biophysica Acta (BBA)-Proteins and Proteomics, vol.1794, pp.375-397, 2009.

P. E. Müller, Limiting Properties of a Continuous Local Mean-Field Interacting Spin System, 2016.

J. D. Murray, Mathematical biology. I, Interdisciplinary Applied Mathematics, vol.17, 2002.

B. Niethammer, Macroscopic limits of the Becker-Döring equations, Commun. Math. Sci, vol.2, issue.1, pp.85-92, 2004.

J. R. Norris, Smoluchowski's coagulation equation: uniqueness, nonuniqueness and a hydrodynamic limit for the stochastic coalescent, Ann. Appl. Probab, vol.9, pp.78-109, 1999.

E. Nummelin, General irreducible Markov chains and nonnegative operators

Y. Ollivier, Ricci curvature of Markov chains on metric spaces, Journal of Functional Analysis, vol.256, pp.810-864, 2009.

F. Oosawa, A. , and S. , Thermodynamics of the polymerization of protein, 1975.

S. Ow and D. E. Dunstan, A brief overview of amyloids and Alzheimer's disease, Protein Science, vol.23, pp.1315-1331, 2014.

G. C. Papanicolaou, D. Stroock, and S. R. Varadhan, Martingale approach to some limit theorems, Papers from the Duke Turbulence Conference, p.120, 1976.

O. Penrose, Metastable states for the Becker-Döring cluster equations, Comm. Math. Phys, vol.124, pp.515-541, 1989.

O. Penrose, Nucleation and droplet growth as a stochastic process, Analysis and stochastics of growth processes and interface models, pp.265-277, 2008.

J. S. Philo, A. , and T. , Mechanisms of protein aggregation, Curr Pharm Biotechnol, vol.10, issue.4, pp.348-351, 2009.

F. Picconi, B. Baynat, and P. Sens, An analytical estimation of durability in DHTs, Distributed Computing and Internet Technology, vol.4882, pp.184-196, 2007.
URL : https://hal.archives-ouvertes.fr/hal-01336258

S. Pigolotti, L. Lizana, D. Otzen, and K. Sneppen, Quality control system response to stochastic growth of amyloid fibrils, FEBS Letters, vol.587, pp.1405-1410, 2013.

E. Pinheiro, W. Weber, and L. A. Barroso, Failure trends in a large disk drive population, 5th USENIX Conference on File and Storage Technologies (FAST'07, pp.17-29, 2007.

J. Pitman, Exchangeable and partially exchangeable random partitions, Probability Theory and Related Fields, vol.102, pp.145-158, 1995.

S. Prigent, A. Ballesta, F. Charles, N. Lenuzza, P. Gabriel et al., An efficient kinetic model for assemblies of amyloid fibrils and its application to polyglutamine aggregation, Plos One, vol.7, p.11, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00778052

L. Pujo-menjouet, Étude de modèles mathématiques issus de la biologie du cycle cellulaire et de la dynamique des protéines. Habilitation à diriger des recherches, 2016.

S. Ramabhadran, P. , and J. , Analysis of long-running replicated systems, Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications, pp.1-9, 2006.

K. Ramanan, Reflected diffusions defined via the extended skorokhod map, Electronic Journal of Probability, vol.11, pp.934-992, 2006.

M. Ranjbar and F. Rezakhanlou, Equilibrium fluctuations for a model of coagulating-fragmenting planar Brownian particles, Comm. Math. Phys, vol.296, issue.3, pp.769-826, 2010.

S. Rhea, B. Godfrey, B. Karp, J. Kubiatowicz, S. Ratnasamy et al., OpenDHT: a public DHT service and its uses, Proceedings of SIGCOMM, pp.73-84, 2005.

P. Robert, Stochastic Networks and Queues. Stochastic Modelling and Applied Probability Series, 2003.

P. Robert and W. Sun, On the asymptotic distribution of nucleation times of polymerization processes, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01672800

R. Rodrigues and C. Blake, When multi-hop peer-to-peer lookup matters, IPTPS'04: Proceedings of the 3rd International Workshop on Peer-to-Peer Systems, pp.112-122, 2004.

L. C. Rogers, D. Williams, and . Diffusions, Markov processes, and martingales, vol.1, 1994.

L. C. Rogers, D. Williams, and . Diffusions, Cambridge Mathematical Library, Markov processes, and martingales, vol.2, 2000.

C. A. Ross and M. A. Poirier, Protein aggregation and neurodegenerative disease, Nat. Med, vol.10, pp.10-17, 2004.

A. I. Rowstron and P. Druschel, Storage management and caching in PAST, a large-scale, persistent peer-to-peer storage utility, the 8th ACM symposium on Operating Systems Principles, pp.188-201, 2001.

W. Rudin, Real and complex analysis, 1987.

T. Shiga and H. Tanaka, Central limit theorem for a system of markovian particles with mean field interactions. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, vol.69, pp.439-459, 1985.

V. Simon, S. Monnet, M. Feuillet, P. Robert, and P. Sens, Scattering and placing data replicas to enhance long-term durability, The 14th IEEE International Symposium on Network Computing and Applications (IEEE NCA15, p.6, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01206960

J. D. Sipe and A. S. Cohen, Review: history of the amyloid fibril, J. Struct. Biol, vol.130, pp.88-98, 2000.

A. Skorokhod, Stochastic equations for diffusion processes in a bounded region, Theory Probab. Appl, vol.7, pp.3-23, 1962.

H. L. Smith, W. Li, and M. E. Cheetham, Molecular chaperones and neuronal proteostasis, Semin. Cell Dev. Biol, vol.40, pp.142-152, 2015.

H. Spohn, Equilibrium fluctuations for interacting brownian particles, Comm. Math. Phys, vol.103, pp.1-33, 1986.

H. Spohn, Large scale dynamics of interacting particles, 2012.

W. Sun, A functional central limit theorem for the becker-döring model, Journal of Statistical Physics, vol.171, issue.1, pp.145-165, 2018.

W. Sun, M. Feuillet, R. , and P. , Analysis of large unreliable stochastic networks, Annals of Applied Probability, vol.26, pp.2959-3000, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01203096

W. Sun, R. , and P. , Analysis of Large Urn Models with Local Mean-Field Interactions, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01710964

W. Sun, V. Simon, S. Monnet, P. Robert, and P. Sens, Analysis of a stochastic model of replication in large distributed storage systems: A mean-field approach, ACM-Sigmetrics, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01494235

J. Szavits-nossan, K. Eden, R. J. Morris, C. E. Macphee, M. R. Evans et al., Inherent variability in the kinetics of autocatalytic protein selfassembly, Physical Review Letters, vol.113, p.98101, 2014.

A. Sznitman, Topics in propagation of chaos, École d'Été de Probabilités de Saint-Flour XIX -1989, vol.1464, pp.167-243, 1991.

A. S. Sznitman, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.66, pp.559-592, 1984.

A. Sznitman, Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated, Journal of Functional Analysis, vol.56, pp.311-336, 1984.

L. Taylor, W. , and R. , Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant, Probability Theory and Related Fields, vol.96, pp.283-317, 1993.

M. Thai, Birth and death process in mean field type interaction, 2015.

M. Von-smoluchowski, Versuch einer mathematischen theorie der koagulationskinetik kolloider lösungen, Zeitschrift fuer physikalische Chemie, vol.92, pp.129-168, 2010.

W. Voter and H. Erickson, The kinetics of microtubule assembly. evidence for a two-stage nucleation mechanism, The Journal of Biological Chemistry, vol.259, pp.10430-10438, 1984.

N. D. Vvedenskaya, R. L. Dobrushin, and F. I. Karpelevich, A queueing system with a choice of the shorter of two queues-an asymptotic approach, Problemy Peredachi Informatsii, vol.32, pp.20-34, 1996.

A. Wegner and J. Engel, Kinetics of the cooperative association of actin to actin filament, Biophysical Chemistry, vol.3, pp.215-225, 1975.

C. Wu and J. E. Shea, Coarse-grained models for protein aggregation, Curr. Opin. Struct. Biol, vol.21, issue.2, pp.209-220, 2011.

W. Xue, S. W. Homans, and S. E. Radford, Systematic analysis of nucleationdependent polymerization reveals new insights into the mechanism of amyloid self-assembly, PNAS, vol.105, pp.8926-8931, 2008.

M. Yor, Existence et unicité de diffusions à valeurs dans un espace de Hilbert, Annales de l'I.H.P. Probabilités et statistiques, vol.10, pp.55-88, 1974.

R. Yvinec, S. Bernard, E. Hingant, and L. Pujo-menjouet, First passage times in homogeneous nucleation: Dependence on the total number of particles, The Journal of Chemical Physics, vol.144, p.34106, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01353266

R. Yvinec, M. R. D'orsogna, and T. Chou, First passage times in homogeneous nucleation and self-assembly, The Journal of Chemical Physics, vol.137, p.244107, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00749630

J. Zhang and M. Muthukumar, Simulations of nucleation and elongation of amyloid fibrils, The Journal of Chemical Physics, vol.130, issue.3, p.35102, 2009.

M. Zhu, Equilibrium fluctuations for one-dimensional Ginzburg-Landau lattice model, Nagoya Math. J, vol.117, pp.63-92, 1990.