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We show that the modified log-Sobolev constant for a natural Markov chain which converges to an $r$-homogeneous strongly log-concave distribution is at least $1/r$.
Balanced matroids
Tomás Feder and Milena Mihail · 1992
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Matroid theory
James G. Oxley · 1992
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Logarithmic Sobolev inequalities for finite Markov chains
Persi Diaconis and Laurent Saloff-Coste · 1996
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Balls and bins: a study in negative dependence
Devdatt Dubhashi and Desh Ranjan · 1998
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Logarithmic Sobolev inequality for some models of random walks
Tzong-Yow Lee and Horng-Tzer Yau · 1998
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Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
Sergey G. Bobkov and Friedrich Götze · 1999
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Counting, sampling and integrating: algorithms and complexity
Mark Jerrum · 2003
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Modified logarithmic Sobolev inequalities for some models of random walk
Sharad Goel · 2004
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Aspects of mass transportation in discrete concentration inequalities
Marcus D. Sammer · 2005
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Modified logarithmic Sobolev inequalities in discrete settings
Sergey G. Bobkov and Prasad Tetali · 2006
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The subgaussian constant and concentration inequalities
Sergey G. Bobkov, Christian Houdré, and Prasad Tetali · 2006
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Polynomials with the half-plane property and matroid theory
Petter Brändén · 2007
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Negative dependence and the geometry of polynomials
Julius Borcea, Petter Brändén, and Thomas M. Liggett · 2009
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Improved mixing time bounds for the Thorp shuffle and L L -reversal chain
Ben Morris · 2009
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Concentration inequalities
Stéphane Boucheron, Gábor Lugosi, and Pascal Massart · 2013
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Markov chains and mixing times
David A. Levin and Yuval Peres · 2017
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Nima Anari, Shayan Oveis Gharan, and Cynthia Vinzant · 2018
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Concentration of Lipschitz functions of negatively dependent variables
Kevin Garbe and Jan Vondrák · 2018
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Correlation bounds for fields and matroids
June Huh, Benjamin Schröter, and Botong Wang · 2018
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High order random walks: Beyond spectral gap
Tali Kaufman and Izhar Oppenheim · 2018
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Improved mixing time bounds for the Thorp shuffle
Ben Morris · 2013
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Concentration of Lipschitz functionals of determinantal and other strong Rayleigh measures
Robin Pemantle and Yuval Peres · 2014
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Monte Carlo Markov chain algorithms for sampling strongly Rayleigh distributions and determinantal point processes
Nima Anari, Shayan Oveis Gharan, and Alireza Rezaei · 2016
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A polynomial-time algorithm to approximate the mixed volume within a simply exponential factor
Leonid Gurvits
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On multivariate Newton-like inequalities
Leonid Gurvits
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A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
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Log-concave polynomials II: high-dimensional walks and an FPRAS for counting bases of a matroid
Nima Anari, Kuikui Liu, Shayan Oveis Gharan, and Cynthia Vinzant · 2019
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