Concentration of measure and mixing for Markov chains

Malwina Luczak

doi:10.46298/dmtcs.3558

Malwina Luczak - Concentration of measure and mixing for Markov chains

dmtcs:3558 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science - https://doi.org/10.46298/dmtcs.3558

Concentration of measure and mixing for Markov chainsArticle

Authors: Malwina Luczak ¹

1 Department of Mathematics London School of Economics

We consider Markovian models on graphs with local dynamics. We show that, under suitable conditions, such Markov chains exhibit both rapid convergence to equilibrium and strong concentration of measure in the stationary distribution. We illustrate our results with applications to some known chains from computer science and statistical mechanics.

https://doi.org/10.46298/dmtcs.3558

Source: HAL:hal-01194679v1

Volume: DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science

Section: Proceedings

Published on: January 1, 2008

Imported on: May 10, 2017

Keywords: Markov chains,concentration of measure,rapid mixing,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

Bibliographic References

12 Documents citing this article

Gesine Reinert;Nathan Ross, 2019, Approximating stationary distributions of fast mixing Glauber dynamics, with applications to exponential random graphs, Project Euclid (Cornell University), 29, 5, 10.1214/19-aap1478, https://projecteuclid.org/euclid.aoap/1571385633.

Radosław Adamczak;Michał Kotowski;Bartłomiej Polaczyk;Michał Strzelecki, 2019, A note on concentration for polynomials in the Ising model, Electronic Journal of Probability, 24, none, 10.1214/19-ejp280, https://doi.org/10.1214/19-ejp280.

Graham Brightwell;Marianne Fairthorne;Malwina J. Luczak, 2018, The Supermarket Model with Bounded Queue Lengths in Equilibrium, Journal of Statistical Physics, 173, 3-4, pp. 1149-1194, 10.1007/s10955-018-2044-7, https://doi.org/10.1007/s10955-018-2044-7.

Reza Gheissari;Eyal Lubetzky;Yuval Peres, 2018, Concentration inequalities for polynomials of contracting Ising models, Electronic Communications in Probability, 23, none, 10.1214/18-ecp173, https://doi.org/10.1214/18-ecp173.

Yevgeniy Kovchegov;Peter T. Otto, SpringerBriefs in probability and mathematical statistics, Large Deviations and Equilibrium Macrostate Phase Transitions, pp. 37-51, 2018, 10.1007/978-3-319-77019-2_3.

Yevgeniy Kovchegov;Peter T. Otto, SpringerBriefs in probability and mathematical statistics, Statistical Mechanical Models and Glauber Dynamics, pp. 23-36, 2018, 10.1007/978-3-319-77019-2_2.

Yevgeniy Kovchegov;Peter T. Otto, SpringerBriefs in probability and mathematical statistics, Aggregate Path Coupling: Higher Dimensional Theory, pp. 65-79, 2018, 10.1007/978-3-319-77019-2_6.

Yevgeniy Kovchegov;Peter T. Otto, SpringerBriefs in probability and mathematical statistics, Coupling, Path Coupling, and Mixing Times, pp. 1-22, 2018, 10.1007/978-3-319-77019-2_1.

Yevgeniy Kovchegov;Peter T. Otto, SpringerBriefs in probability and mathematical statistics, Path Coupling for Curie-Weiss Model, pp. 53-54, 2018, 10.1007/978-3-319-77019-2_4.

Yevgeniy Kovchegov;Peter T. Otto, SpringerBriefs in probability and mathematical statistics, Aggregate Path Coupling: One-Dimensional Theory, pp. 55-64, 2018, 10.1007/978-3-319-77019-2_5.

Yevgeniy Kovchegov;Peter T. Otto, SpringerBriefs in probability and mathematical statistics, Aggregate Path Coupling: Beyond Kn, pp. 81-90, 2018, 10.1007/978-3-319-77019-2_7.

Yevgeniy Kovchegov;Peter T. Otto, 2015, Rapid Mixing of Glauber Dynamics of Gibbs Ensembles via Aggregate Path Coupling and Large Deviations Methods, arXiv (Cornell University), 161, 3, pp. 553-576, 10.1007/s10955-015-1345-3, https://arxiv.org/abs/1312.6728.

Sources : OpenCitations, OpenAlex & Crossref

Share and export

Consultation statistics

This page has been seen 202 times.

This article's PDF has been downloaded 557 times.