Log-Hessian and Deviation Bounds for Markov Semi-Groups, and Regularization Effect in L1
File(s)
Working paper
Author(s)
Gozlan, N
Li, Xue-Mei
Madiman, M
Roberto, C
Samson, P-M
Type
Working Paper
Abstract
In 1989, Talagrand proposed a conjecture regarding the regularization effect
on integrable functions of a natural Markov semigroup on the Boolean hypercube.
While this conjecture remains unresolved, the analogous conjecture for the
Ornstein-Uhlenbeck semigroup was recently resolved by Eldan-Lee and Lehec, by
combining an inequality for the log-Hessian of this semigroup with a new
deviation inequality for log-semiconvex functions under Gaussian measure. Our
first goal is to explore the validity of both these ingredients for some
diffusion semigroups in R n as well as for the M/M/$\infty$ queue on the
non-negative integers. Our second goal is to prove an analogue of Talagrand's
conjecture for these settings, even in those cases where these ingredients are
not valid.
on integrable functions of a natural Markov semigroup on the Boolean hypercube.
While this conjecture remains unresolved, the analogous conjecture for the
Ornstein-Uhlenbeck semigroup was recently resolved by Eldan-Lee and Lehec, by
combining an inequality for the log-Hessian of this semigroup with a new
deviation inequality for log-semiconvex functions under Gaussian measure. Our
first goal is to explore the validity of both these ingredients for some
diffusion semigroups in R n as well as for the M/M/$\infty$ queue on the
non-negative integers. Our second goal is to prove an analogue of Talagrand's
conjecture for these settings, even in those cases where these ingredients are
not valid.
Date Issued
2019-07-25
Date Acceptance
2021-05-19
Citation
Potential Analysis
ISSN
0926-2601
Publisher
Springer
Journal / Book Title
Potential Analysis
Copyright Statement
© 2019 The Author(s)
Identifier
http://arxiv.org/abs/1907.10896v1
Subjects
math.PR
math.PR
Publication Status
Accepted