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math.PR2022
Upgrading MLSI to LSI for reversible Markov chains
Justin Salez, Konstantin Tikhomirov, Pierre Youssef
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 l…
math.PR2022★ 1 cited
Regularized modified log-Sobolev inequalities, and comparison of Markov chains
Konstantin Tikhomirov, Pierre Youssef
In this work, we develop a comparison procedure for the Modified log-Sobolev Inequality (MLSI) constants of two reversible Markov chains on a finite state space. Efficient comparis…
math.PR2022
Quantitative invertibility of non-Hermitian random matrices
Konstantin Tikhomirov
The problem of estimating the smallest singular value of random square matrices is important in connection with matrix computations and analysis of the spectral distribution. In th…