D. Aldous and J. Fill, Reversible markov chains and random walks on graphs, 2002.

D. A. Levin, Y. Peres, and E. L. Wilmer, Markov chains and mixing times, 2009.
DOI : 10.1090/mbk/058

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, Equation of State Calculations by Fast Computing Machines, The Journal of Chemical Physics, vol.21, issue.6, pp.1087-1092, 1953.
DOI : 10.1063/1.1700747

W. K. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika, vol.57, issue.1, pp.97-109, 1970.
DOI : 10.1093/biomet/57.1.97

F. Martinelli, Lectures on Glauber Dynamics for Discrete Spin Models, Lectures on probability theory and statistics, pp.93-191, 1999.
DOI : 10.1007/978-3-540-48115-7_2

M. Dyer, A. Frieze, and R. Kannan, A random polynomial-time algorithm for approximating the volume of convex bodies, Journal of the ACM, vol.38, issue.1, pp.1-17, 1991.
DOI : 10.1145/102782.102783

M. Jerrum, A. Sinclair, and E. Vigoda, A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries, Journal of the ACM, vol.51, issue.4, pp.671-697, 2004.
DOI : 10.1145/1008731.1008738

P. Diaconis, The cutoff phenomenon in finite Markov chains., Proceedings of the National Academy of Sciences, vol.93, issue.4, pp.1659-1664, 1996.
DOI : 10.1073/pnas.93.4.1659

P. Diaconis, S. Holmes, and R. M. Neal, Analysis of a nonreversible Markov chain sampler, The Annals of Applied Probability, vol.10, issue.3, pp.726-752, 2000.
DOI : 10.1214/aoap/1019487508

F. Chen, L. Lovász, and I. Pak, Lifting Markov chains to speed up mixing, Proceedings of the thirty-first annual ACM symposium on Theory of computing , STOC '99, pp.275-281, 1999.
DOI : 10.1145/301250.301315

URL : http://www.cs.yale.edu/HTML/YALE/CS/HyPlans/lovasz/liftst99.ps

P. Diaconis and L. Miclo, On the spectral analysis of second-order Markov chains, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.22, issue.3, pp.573-621, 2013.
DOI : 10.5802/afst.1383

URL : https://hal.archives-ouvertes.fr/hal-00719047

M. Vucelja, Lifting???A nonreversible Markov chain Monte Carlo algorithm, American Journal of Physics, vol.84, issue.12, pp.958-968, 2016.
DOI : 10.1119/1.4961596

URL : http://arxiv.org/pdf/1412.8762

N. Alon, I. Benjamini, E. Lubetzky, and S. Sodin, NON-BACKTRACKING RANDOM WALKS MIX FASTER, Communications in Contemporary Mathematics, vol.23, issue.04, pp.585-603, 2007.
DOI : 10.1017/S0963548300000390

K. Jung, D. Shah, and J. Shin, Distributed Averaging Via Lifted Markov Chains, IEEE Transactions on Information Theory, vol.56, issue.1, pp.634-647, 2010.
DOI : 10.1109/TIT.2009.2034777

URL : http://web.kaist.ac.kr/~kyomin/IT09_lifting.pdf

K. S. Turitsyn, M. Chertkov, and M. Vucelja, Irreversible Monte Carlo algorithms for efficient sampling, Physica D: Nonlinear Phenomena, vol.240, issue.4-5, pp.410-414, 2011.
DOI : 10.1016/j.physd.2010.10.003

URL : http://arxiv.org/pdf/0809.0916

H. C. Fernandes and M. Weigel, Non-reversible Monte Carlo simulations of spin models, Computer Physics Communications, vol.182, issue.9, pp.1856-1859, 2011.
DOI : 10.1016/j.cpc.2010.11.017

Y. Sakai and K. Hukushima, Eigenvalue analysis of an irreversible random walk with skew detailed balance conditions, Physical Review E, vol.93, issue.4, p.43318, 2016.
DOI : 10.1103/PhysRevE.88.020101

URL : http://arxiv.org/pdf/1511.08100

M. Pavon and F. Ticozzi, Discrete-time classical and quantum Markovian evolutions: Maximum entropy problems on path space, Journal of Mathematical Physics, vol.1, issue.4, p.42104, 2010.
DOI : 10.1103/PhysRevA.33.1532

URL : http://arxiv.org/pdf/0811.0933

B. Gerencsér, Markov chain mixing time on cycles, Stochastic Processes and their Applications, pp.2553-2570, 2011.
DOI : 10.1016/j.spa.2011.07.007

L. Rabiner and B. Juang, An introduction to hidden Markov models, ieee assp magazine, pp.4-16, 1986.
DOI : 10.1109/MASSP.1986.1165342

T. T. Georgiou and M. Pavon, Positive contraction mappings for classical and quantum Schr??dinger systems, Journal of Mathematical Physics, vol.3, issue.84, p.33301, 2015.
DOI : 10.1109/TAC.1986.1104412

URL : http://arxiv.org/pdf/1405.6650

J. Kempe, Quantum random walks: An introductory overview, Contemporary Physics, vol.44, issue.4, pp.307-327, 2003.
DOI : 10.1080/00107151031000110776