Upgrading MLSI to LSI for reversible Markov chains

Justin Salez, Konstantin Tikhomirov, Pierre Youssef

Research output: Working paperPreprint


For reversible Markov chains on finite state spaces, we show that the modified log-Sobolev inequality (MLSI) can be upgraded to a log-Sobolev inequality (LSI) at the surprisingly low cost of degrading the associated constant by $\log (1/p)$, where $p$ is the minimum non-zero transition probability. We illustrate this by providing the first log-Sobolev estimate for Zero-Range processes on arbitrary graphs. As another application, we determine the modified log-Sobolev constant of the Lamplighter chain on all bounded-degree graphs, and use it to provide negative answers to two open questions by Montenegro and Tetali (2006) and Hermon and Peres (2018). Our proof builds upon the `regularization trick' recently introduced by the last two authors.
Original languageEnglish
StatePublished - Dec 12 2022


  • math.PR
  • math.CO
  • math.FA
  • 60J27 (Primary) 60J46, 46E39 (Secondary)


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