C. Bardos, R. Santos, and R. Sentis, Diffusion approximation and computation of the critical size, Transactions of the American Mathematical Society, vol.284, issue.2, pp.617-649, 1984.
DOI : 10.1090/S0002-9947-1984-0743736-0

N. B. Abdallah, A. Mellet, and M. Puel, ANOMALOUS DIFFUSION LIMIT FOR KINETIC EQUATIONS WITH DEGENERATE COLLISION FREQUENCY, Mathematical Models and Methods in Applied Sciences, vol.21, issue.11, pp.2249-2262, 2011.
DOI : 10.1142/S0218202511005738

N. B. Abdallah, A. Mellet, and M. Puel, Fractional diffusion limit for collisional kinetic equations : A Hilbert expansion approach. Kinetic and related models, pp.873-900, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00807757

A. Bensoussan, J. L. Lions, and G. Papanicolaou, Boundary layers and homogenization of transport processes, Publications of the Research Institute for Mathematical Sciences, vol.15, issue.1, pp.53-157, 1979.
DOI : 10.2977/prims/1195188427

A. V. Bobylev, J. A. Carrillo, and I. M. Gamba, On some properties of kinetic and hydrodynamic equations for inelastic interactions, Journal of Statistical Physics, vol.98, issue.3/4, pp.743-773, 2000.
DOI : 10.1023/A:1018627625800

A. V. Bobylev and I. M. Gamba, Boltzmann Equations For Mixtures of Maxwell Gases: Exact Solutions and Power Like Tails, Journal of Statistical Physics, vol.15, issue.7, pp.497-516, 2006.
DOI : 10.1007/s10955-006-9044-8

J. A. Carrillo, T. Goudon, P. Lafitte, and F. Vecil, Numerical Schemes of Diffusion Asymptotics and??Moment Closures for Kinetic Equations, Journal of Scientific Computing, vol.1, issue.1, pp.113-149, 2008.
DOI : 10.1007/s10915-007-9181-5

URL : https://hal.archives-ouvertes.fr/hal-00768401

N. Crouseilles, H. Hivert, and M. Lemou, Multiscale numerical schemes for kinetic equations in the anomalous diffusion limit, Comptes Rendus Mathematique, vol.353, issue.8, pp.755-760, 2015.
DOI : 10.1016/j.crma.2015.05.003

URL : https://hal.archives-ouvertes.fr/hal-01151518

N. Crouseilles, H. Hivert, and M. Lemou, Numerical Schemes for Kinetic Equations in the Anomalous Diffusion Limit. Part I: The Case of Heavy-Tailed Equilibrium, SIAM Journal on Scientific Computing, vol.38, issue.2, 2015.
DOI : 10.1137/15M1011366

URL : https://hal.archives-ouvertes.fr/hal-01151518

P. Degond, T. Goudon, and F. Poupaud, Diffusion limit for non homogeneous and non-microreversible processes, Indiana Univ. Math. J, vol.49, pp.1175-1198, 2000.

D. Del-castillo-negrete, B. Carreras, and V. Lynch, Nondiffusive Transport in Plasma Turbulence: A Fractional Diffusion Approach, Physical Review Letters, vol.94, issue.6, p.65003, 2005.
DOI : 10.1103/PhysRevLett.94.065003

M. H. Ernst and R. Brito, Scaling solutions of inelastic Boltzmann equations with overpopulated high energy tails, J. Stat. Phys, vol.109, pp.3-4407, 2002.

M. Jara, T. Komorowski, and S. Olla, Limit theorems for additive functionals of a Markov chain, The Annals of Applied Probability, vol.19, issue.6, pp.2270-2300, 2009.
DOI : 10.1214/09-AAP610

URL : https://hal.archives-ouvertes.fr/hal-00315784

S. Jin, Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations, SIAM Journal on Scientific Computing, vol.21, issue.2, pp.441-454, 1999.
DOI : 10.1137/S1064827598334599

S. Jin, L. Pareschi, and G. Toscani, Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations, SIAM Journal on Numerical Analysis, vol.38, issue.3, pp.913-936, 2000.
DOI : 10.1137/S0036142998347978

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.1966

A. Klar, An Asymptotic-Induced Scheme for Nonstationary Transport Equations in the Diffusive Limit, 28 N. CROUSEILLES, H. HIVERT AND M. LEMOU, pp.1073-1094, 1998.
DOI : 10.1137/S0036142996305558

C. Kleiber and S. Kotz, Statistical size distributions in economics and actuarial sciences, 2003.
DOI : 10.1002/0471457175

E. W. Larsen and J. B. Keller, Asymptotic solution of neutron transport problems for small mean free paths, Journal of Mathematical Physics, vol.15, issue.1, pp.75-81, 1974.
DOI : 10.1063/1.1666510

M. Lemou and F. Méhats, Micro-Macro Schemes for Kinetic Equations Including Boundary Layers, SIAM Journal on Scientific Computing, vol.34, issue.6, pp.734-760, 2012.
DOI : 10.1137/120865513

URL : https://hal.archives-ouvertes.fr/hal-00751788

M. Lemou and L. Mieussens, A New Asymptotic Preserving Scheme Based on Micro-Macro Formulation for Linear Kinetic Equations in the Diffusion Limit, SIAM Journal on Scientific Computing, vol.31, issue.1, pp.334-368, 2008.
DOI : 10.1137/07069479X

URL : https://hal.archives-ouvertes.fr/hal-00348594

A. Mellet, Fractional diffusion limit for collisional kinetic equations: A moments method, Indiana University Mathematics Journal, vol.59, issue.4, pp.1333-1360, 2010.
DOI : 10.1512/iumj.2010.59.4128

A. Mellet and S. Merino-aceituno, Anomalous Energy Transport in FPU- $$\beta $$ ?? Chain, Journal of Statistical Physics, vol.154, issue.5, pp.1-39
DOI : 10.1007/s10955-015-1273-2

A. Mellet, S. Mischler, and C. Mouhot, Fractional Diffusion Limit for Collisional Kinetic Equations, Archive for Rational Mechanics and Analysis, vol.346, issue.2, pp.493-525, 2011.
DOI : 10.1007/s00205-010-0354-2

URL : https://hal.archives-ouvertes.fr/hal-00321478

L. Mieussens, On the asymptotic preserving property of the unified gas kinetic scheme for the diffusion limit of linear kinetic models, Journal of Computational Physics, vol.253, pp.138-156, 2013.
DOI : 10.1016/j.jcp.2013.07.002

URL : https://hal.archives-ouvertes.fr/hal-00772684

G. Naldi and L. Pareschi, Numerical schemes for kinetic equations in diffusive regimes, Applied Mathematics Letters, vol.11, issue.2, pp.29-35, 1998.
DOI : 10.1016/S0893-9659(98)00006-8

L. Wang and B. Yan, An asymptotic-preserving scheme for linear kinetic equation with fractional diffusion limit, Journal of Computational Physics, vol.312, 2015.
DOI : 10.1016/j.jcp.2016.02.034

E. Wigner, Nuclear reactor theory, 1961.