Swendsen-Wang dynamics for general graphs in the tree uniqueness region

[1]  A. Sinclair,et al.  Spatial mixing and the connective constant: optimal bounds , 2015, SODA 2015.

[2]  A. D. Sokal,et al.  Dynamic critical behavior of a Swendsen-Wang-Type algorithm for the Ashkin-Teller model , 1996 .

[3]  E. Ising Beitrag zur Theorie des Ferromagnetismus , 1925 .

[4]  A. Sokal,et al.  Generalization of the Fortuin-Kasteleyn-Swendsen-Wang representation and Monte Carlo algorithm. , 1988, Physical review. D, Particles and fields.

[5]  Y. Peres,et al.  Markov Chains and Mixing Times: Second Edition , 2017 .

[6]  Alan D. Sokal,et al.  Dynamic critical behavior of the Swendsen-Wang algorithm: The two-dimensional three-state Potts model revisited , 1997 .

[7]  F. Martinelli,et al.  Approach to equilibrium of Glauber dynamics in the one phase region , 1994 .

[8]  Eric Vigoda,et al.  Spatial mixing and nonlocal Markov chains , 2017, SODA.

[9]  Alan M. Frieze,et al.  Torpid mixing of some Monte Carlo Markov chain algorithms in statistical physics , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[10]  Jian-Sheng Wang Critical dynamics of the Swendsen-Wang algorithm in the three-dimensional Ising model , 1990 .

[11]  Allan Sly,et al.  Computational Transition at the Uniqueness Threshold , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.

[12]  F. Cesi Quasi-factorization of the entropy and logarithmic Sobolev inequalities for Gibbs random fields , 2001 .

[13]  Y. Peres,et al.  Mixing time for the Ising model: A uniform lower bound for all graphs , 2009, 0909.5162.

[14]  James Allen Fill,et al.  Comparison inequalities and fastest-mixing Markov chains , 2011, 1109.6075.

[15]  Dror Weitz,et al.  Counting independent sets up to the tree threshold , 2006, STOC '06.

[16]  Christian Borgs,et al.  Tight bounds for mixing of the Swendsen–Wang algorithm at the Potts transition point , 2010, ArXiv.

[17]  Elchanan Mossel,et al.  Exact thresholds for Ising–Gibbs samplers on general graphs , 2009, The Annals of Probability.

[18]  Yuval Peres,et al.  Exponentially slow mixing in the mean-field Swendsen-Wang dynamics , 2017, SODA.

[19]  Y. Peres,et al.  Mixing Time of Critical Ising Model on Trees is Polynomial in the Height , 2009, 0901.4152.

[20]  F. Martinelli,et al.  Approach to equilibrium of Glauber dynamics in the one phase region , 1994 .

[21]  Alexander E. Holroyd Some Circumstances Where Extra Updates Can Delay Mixing , 2011 .

[22]  M. Jerrum,et al.  The Swendsen–Wang Process Does Not Always Mix Rapidly , 1999 .

[23]  Mark Jerrum,et al.  Random cluster dynamics for the Ising model is rapidly mixing , 2016, SODA.

[24]  Leslie G. Valiant,et al.  Random Generation of Combinatorial Structures from a Uniform Distribution , 1986, Theor. Comput. Sci..

[25]  Y. Peres,et al.  Can Extra Updates Delay Mixing? , 2011, 1112.0603.

[26]  F. Martinelli,et al.  For 2-D lattice spin systems weak mixing implies strong mixing , 1994 .

[27]  Eric Vigoda,et al.  A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries , 2004, JACM.

[28]  Glenn Ellison Learning, Local Interaction, and Coordination , 1993 .

[29]  M. Simonovits,et al.  Random walks and an O * ( n 5 ) volume algorithm for convex bodies , 1997 .

[30]  Martin E. Dyer,et al.  Mixing in time and space for lattice spin systems: A combinatorial view , 2002, International Workshop Randomization and Approximation Techniques in Computer Science.

[31]  Liang Li,et al.  Correlation Decay up to Uniqueness in Spin Systems , 2013, SODA.

[32]  Mark Jerrum,et al.  Polynomial-Time Approximation Algorithms for the Ising Model , 1990, SIAM J. Comput..

[33]  Eric Vigoda,et al.  Adaptive Simulated Annealing: A Near-optimal Connection between Sampling and Counting , 2006, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).

[34]  Andrea Montanari,et al.  The spread of innovations in social networks , 2010, Proceedings of the National Academy of Sciences.

[35]  Wang,et al.  Nonuniversal critical dynamics in Monte Carlo simulations. , 1987, Physical review letters.

[36]  Mario Ullrich Rapid mixing of Swendsen–Wang dynamics in two dimensions , 2012, 1212.4908.

[37]  Piyush Srivastava,et al.  Approximation Algorithms for Two-State Anti-Ferromagnetic Spin Systems on Bounded Degree Graphs , 2011, Journal of Statistical Physics.

[38]  Thomas P. Hayes,et al.  A general lower bound for mixing of single-site dynamics on graphs , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[39]  Asaf Nachmias,et al.  A power law of order 1/4 for critical mean-field Swendsen-Wang dynamics , 2011 .

[40]  Allan Sly,et al.  The Computational Hardness of Counting in Two-Spin Models on d-Regular Graphs , 2012, 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science.

[41]  Elchanan Mossel,et al.  Evolutionary trees and the Ising model on the Bethe lattice: a proof of Steel’s conjecture , 2005, ArXiv.