Fetching the paper…
Reading the bibliography…
We introduce a framework for obtaining tight mixing times for Markov chains based on what we call restricted modified log-Sobolev inequalities.
“The problem of uniqueness of a Gibbsian random field and the problem of phase transitions”
Roland’vovich Dobrushin · 1968
Earlier work this paper cites.
“Constructive criterion for the uniqueness of Gibbs field”
Roland Dobrushin and Senya Shlosman · 1985
Earlier work this paper cites.
“Spin glass theory and beyond: An Introduction to the Replica Method and Its Applications”
Marc Mézard, Giorgio Parisi and Miguel Virasoro · 1987
Earlier work this paper cites.
“Poincaré and transportation inequalities for Gibbs measures under the Dobrushin uniqueness condition”
Liming Wu · 1989
Earlier work this paper cites.
“The equivalence of the logarithmic Sobolev inequality and the Dobrushin-Shlosman mixing condition”
Daniel Stroock and Boguslaw Zegarlinski · 1992
Earlier work this paper cites.
“Dobrushin uniqueness theorem and logarithmic Sobolev inequalities”
Boguslaw Zegarlinski · 1992
Earlier work this paper cites.
“Exponential integrability and transportation cost related to logarithmic Sobolev inequalities”
Sergej Bobkov and Friedrich Götze · 1999
Earlier work this paper cites.
“On counting independent sets in sparse graphs”
Martin Dyer, Alan Frieze and Mark Jerrum · 2002
Earlier work this paper cites.
“Transportation cost-information inequalities and applications to random dynamical systems and diffusions”
Hacene Djellout, Arnaud Guillin and Liming Wu · 2004
Earlier work this paper cites.
“Modified logarithmic Sobolev inequalities for some models of random walk”
Sharad Goel · 2004
Earlier work this paper cites.
“Measure concentration for Euclidean distance in the case of dependent random variables”
Katalin Marton · 2004
Earlier work this paper cites.
“Modified logarithmic Sobolev inequalities in discrete settings”
Sergey Bobkov and Prasad Tetali · 2006
Earlier work this paper cites.
“Systematic scan for sampling colorings”
Martin Dyer, Leslie Goldberg and Mark Jerrum · 2006
Earlier work this paper cites.
“A simple condition implying rapid mixing of single-site dynamics on spin systems”
Thomas Hayes · 2006
Earlier work this paper cites.
“Coupling with the stationary distribution and improved sampling for colorings and independent sets”
Thomas Hayes and Eric Vigoda · 2006
Earlier work this paper cites.
“Counting independent sets up to the tree threshold”
Dror Weitz · 2006
Earlier work this paper cites.
“Iterative hard thresholding for compressed sensing”
Thomas Blumensath and Mike Davies · 2009
Earlier work this paper cites.
“On the hardness of sampling independent sets beyond the tree threshold”
Elchanan Mossel, Dror Weitz and Nicholas Wormald · 2009
Earlier work this paper cites.
“Computational transition at the uniqueness threshold”
Allan Sly · 2010
Cited alongside, same era.
“Simulating events of unknown probabilities via reverse time martingales”
Krzysztof Łatuszyński, Ioannis Kosmidis, Omiros Papaspiliopoulos and Gareth Roberts · 2011
Cited alongside, same era.
“Correlation Decay up to Uniqueness in Spin Systems”
Liang Li, Pinyan Lu and Yitong Yin · 2011
Cited alongside, same era.
“The computational hardness of counting in two-spin models on d-regular graphs”
Allan Sly and Nike Sun · 2012
Cited alongside, same era.
“Entropy decay for interacting systems via the Bochner-Bakry-Émery approach”
Paolo Dai and Gustavo Posta · 2013
Cited alongside, same era.
“Exact thresholds for Ising–Gibbs samplers on general graphs”
“High order random walks: Beyond spectral gap”
Tali Kaufman and Izhar Oppenheim · 2018
Later among the works it cites.
“Log-Concave Polynomials II: High-Dimensional Walks and an FPRAS for Counting Bases of a Matroid”
Nima Anari, Kuikui Liu, Shayan Oveis and Cynthia Vinzant · 2019
Later among the works it cites.
“A very simple proof of the LSI for high temperature spin systems”
Roland Bauerschmidt and Thierry Bodineau · 2019
Later among the works it cites.
Petter Brändén and June Huh · 2019
Later among the works it cites.
“Convergence of MCMC and loopy BP in the tree uniqueness region for the hard-core model”
Charilaos Efthymiou et al · 2019
Later among the works it cites.
“Modified log-Sobolev inequalities for strong-Rayleigh measures”
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Elchanan Mossel and Allan Sly · 2013
Cited alongside, same era.
“Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs”
Alistair Sinclair, Piyush Srivastava and Marc Thurley · 2014
Cited alongside, same era.
“Entropy, optimization and counting”
Mohit Singh and Nisheeth Vishnoi · 2014
Cited alongside, same era.
“Probability in high dimension”, 2014
Ramon Van · 2014
Cited alongside, same era.
“Approximate tensorization of entropy at high temperature”
Pietro Caputo, Georg Menz and Prasad Tetali · 2015
Cited alongside, same era.
Katalin Marton · 2015
Cited alongside, same era.
“Inapproximability of the partition function for the antiferromagnetic Ising and hard-core models”
Andreas Galanis, Daniel Štefankovič and Eric Vigoda · 2016
Cited alongside, same era.
Jonathan Hermon and Justin Salez · 2019
Later among the works it cites.
“Isotropy and Log-Concave Polynomials: Accelerated Sampling and High-Precision Counting of Matroid Bases”
Nima Anari and Michał Dereziński · 2020
Later among the works it cites.
“Improved analysis of higher order random walks and applications”
Vedat Alev and Lap Lau · 2020
Later among the works it cites.
“Spectral Independence in High-Dimensional Expanders and Applications to the Hardcore Model”
Nima Anari, Kuikui Liu and Shayan Oveis · 2020
Later among the works it cites.
“Rapid mixing of Glauber dynamics up to uniqueness via contraction”
Zongchen Chen, Kuikui Liu and Eric Vigoda · 2020
Later among the works it cites.
“Fractionally Log-Concave and Sector-Stable Polynomials: Counting Planar Matchings and More”
Yeganeh Alimohammadi, Nima Anari, Kirankumar Shiragur and Thuy-Duong Vuong · 2021
Closest in time.
“Spectral independence in high-dimensional expanders and applications to the hardcore model”
Nima Anari, Kuikui Liu and Shayan Oveis · 2021
Closest in time.
Nima Anari et al · 2021
Closest in time.
“On mixing of Markov chains: Coupling, spectral independence, and entropy factorization”
Antonio Blanca et al · 2021
Closest in time.
“Rapid mixing of Glauber dynamics via spectral independence for all degrees”, 2021
Xiaoyu Chen, Weiming Feng, Yitong Yin and Xinyuan Zhang · 2021
Closest in time.
“Optimal mixing of Glauber dynamics: Entropy factorization via high-dimensional expansion”
Zongchen Chen, Kuikui Liu and Eric Vigoda · 2021
Closest in time.
“A spectral condition for spectral gap: fast mixing in high-temperature Ising models”
Ronen Eldan, Frederic Koehler and Ofer Zeitouni · 2021
Closest in time.