Fetching the paper…
Reading the bibliography…
For general spin systems, we prove that a contractive coupling for any local Markov chain implies optimal bounds on the mixing time and the modified log-Sobolev constant for a large class of Markov chains including the Glauber dynamics, arbitrary heat-bath block dynamics, and the Swendsen-Wang dynamics.
“On the random-cluster model I. Introduction and relation to other models”
C.. Fortuin and P.. Kasteleyn · 1972
Earlier work this paper cites.
“Nonuniversal critical dynamics in Monte Carlo simulations”
R.. Swendsen and J.. Wang · 1987
Earlier work this paper cites.
“The equivalence of the logarithmic Sobolev inequality and the Dobrushin-Shlosman mixing condition”
D.. Stroock and B. Zegarlinski · 1992
Earlier work this paper cites.
“Approach to equilibrium of Glauber dynamics in the one phase region. II. The general case”
F. Martinelli and E. Olivieri · 1994
Earlier work this paper cites.
“A very simple algorithm for estimating the number of k k -colorings of a low-degree graph”
M. Jerrum · 1995
Earlier work this paper cites.
“Logarithmic Sobolev inequalities for finite Markov chains”
P. Diaconis and L. Saloff-Coste · 1996
Earlier work this paper cites.
“The random-cluster model on a homogeneous tree”
O. H“”aggstr“”om · 1996
Earlier work this paper cites.
“Path coupling: a technique for proving rapid mixing in Markov chains”
R. Bubley and M.. Dyer · 1997
Earlier work this paper cites.
“Concentration of measure and logarithmic Sobolev inequalities”
M. Ledoux · 1999
Earlier work this paper cites.
“Lectures on Glauber dynamics for discrete spin models”
F. Martinelli · 1999
Earlier work this paper cites.
“Matrix analysis and applied linear algebra”
C.. Meyer · 2000
Earlier work this paper cites.
“Improved bounds for sampling colorings”
E. Vigoda · 2000
Earlier work this paper cites.
“Quasi-factorization of the entropy and logarithmic Sobolev inequalities for Gibbs random fields”
F. Cesi · 2001
Earlier work this paper cites.
“Relaxation time of anisotropic simple exclusion processes and quantum Heisenberg models”
P. Caputo and F. Martinelli · 2003
Earlier work this paper cites.
“Determination of the spectral gap for Kac’s master equation and related stochastic evolution”
E.. Carlen, M.. Carvalho and M. Loss · 2003
Earlier work this paper cites.
“Spectral gap inequalities in product spaces with conservation laws”
P. Caputo · 2004
Earlier work this paper cites.
“A sharp analog of Young’s inequality on S N {S}^{N} and related entropy inequalities”
E.. Carlen, E.. Lieb and M. Loss · 2004
Earlier work this paper cites.
“Modified logarithmic Sobolev inequalities in discrete settings”
S. Bobkov and P. Tetali · 2006
Cited alongside, same era.
“The Random-Cluster Model”
G.. Grimmett · 2006
Cited alongside, same era.
“A simple condition implying rapid mixing of single-site dynamics on spin systems”
T.. Hayes · 2006
Cited alongside, same era.
“A general lower bound for mixing of single-site dynamics on graphs”
T.. Hayes and A. Sinclair · 2007
Cited alongside, same era.
“Subadditivity of the entropy and its relation to Brascamp-Lieb type inequalities”
E.. Carlen and D. Cordero-Erasquin · 2009
Cited alongside, same era.
“Matrix norms and rapid mixing for spin systems”
M. Dyer, L.. Goldberg and M. Jerrum · 2009
Cited alongside, same era.
“Stein’s method for stationary distributions of Markov chains and application to Ising models”
G. Bresler and D. Nagaraj · 2019
Later among the works it cites.
“Improved bounds for randomly sampling colorings via linear programming”
S. Chen, M. Delcourt, A. Moitra, G. Perarnau and L. Postle · 2019
Later among the works it cites.
“Higher order concentration for functions of weakly dependent random variables”
F. G“”otze, H. Sambale and A. Sinulis · 2019
Later among the works it cites.
“Modified log-Sobolev inequalities for strong-Rayleigh measures”
J. Hermon and J. Salez · 2019
Later among the works it cites.
“Logarithmic Sobolev inequalities in discrete product spaces”
K. Marton · 2019
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
“Ricci curvature of Markov chains on metric spaces”
Y. Ollivier · 2009
Cited alongside, same era.
“Correlation and Brascamp-Lieb inequalities for Markov semigroups”
F. Barthe, D. Cordero-Erausquin, M. Ledoux and B. Maurey · 2011
Cited alongside, same era.
“On continuous dependence of roots of polynomials on coefficients” Technical notes, 2013
A. Alexanderian · 2013
Cited alongside, same era.
“Exact thresholds for Ising–Gibbs samplers on general graphs”
E. Mossel and A. Sly · 2013
Cited alongside, same era.
“Rapid mixing of Swendsen-Wang dynamics in two dimensions”
M. Ullrich · 2014
Cited alongside, same era.
“Approximate tensorization of entropy at high temperature”
P. Caputo, G. Menz and P. Tetali · 2015
Cited alongside, same era.
G. Reinert and N. Ross · 2019
Later among the works it cites.
“Spectral Independence in High-Dimensional Expanders and Applications to the Hardcore Model”
N. Anari, K. Liu and S. Oveis Gharan · 2020
Later among the works it cites.
“Swendsen-Wang dynamics for general graphs in the tree uniqueness region”
A. Blanca, Z. Chen and E. Vigoda · 2020
Later among the works it cites.
“Block factorization of the relative entropy via spatial mixing”
P. Caputo and D. Parisi · 2020
Later among the works it cites.
“Rapid Mixing of Glauber Dynamics up to Uniqueness via Contraction”
Z. Chen, K. Liu and E. Vigoda · 2020
Later among the works it cites.
“Logarithmic Sobolev inequalities for finite spin systems and applications”
H. Sambale and A. Sinulis · 2020
Later among the works it cites.
“Entropy decay in the Swendsen-Wang dynamics”
A. Blanca, P. Caputo, D. Parisi, A. Sinclair and E. Vigoda · 2021
Closest in time.
“Optimal Mixing of Glauber Dynamics: Entropy Factorization via High-Dimensional Expansion”
Z. Chen, K. Liu and E. Vigoda · 2021
Closest in time.
“Rapid Mixing for Colorings via Spectral Independence”
Z. Chen, A. Galanis, D. Stefankovic and E. Vigoda · 2021
Closest in time.
“Modified log-Sobolev inequalities for strongly log-concave distributions”
M. Cryan, H. Guo and G. Mousa · 2021
Closest in time.
“Rapid mixing from spectral independence beyond the Boolean domain”
W. Feng, H. Guo, Y. Yin and C. Zhang · 2021
Closest in time.