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Logarithmic Sobolev, isoperimetry and transport inequalities on graphs

2016
*
Acta Mathematica Sinica. English series
*

We provide estimates of

doi:10.1007/s10114-016-5330-9
fatcat:qhzj2rtdw5ez7kal4sf3ol5ogi
*the*involved*constants*. ... transportation-entropy inequality)*for*reversible nearest-neighbor Markov processes on connected finite graphs by means of (random)*path**method*. ... Acknowledgements*The*authors are grateful to*the*anonymous referees*for*constructive comments and corrections.*Logarithmic**Sobolev*, Isoperimetry and Transport Inequalities on Graphs ...##
###
Log-Sobolev, isoperimetry and transport inequalities on graphs
[article]

2015
*
arXiv
*
pre-print

and transportation-entropy inequalities)

arXiv:1505.04552v1
fatcat:plkovrl7xzhgrdruhwsnw6phwe
*for*reversible nearest-neighbor Markov processes on*a*connected finite graph by means of (random)*path**method*. ... We provide estimates of*the*involved*constants*. ...*The*upper bound in (2.4) gives us*a*very practical criterion*for**the**logarithmic**Sobolev*inequality, following*the*classical idea of Lyapunov function*method**for*stability. ...##
###
Logarithmic Harnack Inequalities

1996
*
Mathematical Research Letters
*

*The*problem of bounding log-

*Sobolev*

*constants*tends to be harder than estimating eigenvalues.

*Logarithmic*Harnack inequalities provide

*a*direct approach

*for*estimating

*the*log-

*Sobolev*

*constant*. ... We will establish

*Logarithmic*Harnack inequalities which can be used to derive lower bounds

*for*log-

*Sobolev*

*constants*. ... Many

*methods*

*for*bounding log-

*Sobolev*

*constants*

*for*graphs can be extended to

*the*log-

*Sobolev*

*constant*

*for*certain subgraphs as well. ...

##
###
Page 5069 of Mathematical Reviews Vol. , Issue 97H
[page]

1997
*
Mathematical Reviews
*

*The*main result,

*the*

*logarithmic*

*Sobolev*inequality, states that there exists

*a*

*constant*C > 0 (depending on G and

*the*metric) such that

*for*all bounded cylinder functions f on 7(G), g € Z(G) and T>0, ... Under this setting, it is shown that several previously developed

*methods*may be applied to give

*a*

*logarithmic*

*Sobolev*inequality without potential term. ...

##
###
Logarithmic Sobolev and Poincaré inequalities for the circular Cauchy distribution

2014
*
Electronic Communications in Probability
*

In this paper, we consider

doi:10.1214/ecp.v19-3071
fatcat:xt6jymc27jalbbxt3fc3hbizxa
*the*circular Cauchy distribution µx on*the*unit circle S with index 0 ≤ |x| < 1 and we study*the*spectral gap and*the*optimal*logarithmic**Sobolev**constant**for*µx, denoted respectively ... first inequality is true since*the*optimal*logarithmic**Sobolev**constant**for**the*Bernoulli distribution with parameter 1/2 is 1. ... We will denote by C LS (µ x )*the*optimal*logarithmic**Sobolev**constant*of µ x . ...##
###
Page 3262 of Mathematical Reviews Vol. , Issue 93f
[page]

1993
*
Mathematical Reviews
*

*The*

*constant*Cr can be chosen in- dependent of 7,

*for*T small.

*The*author’s proof also involves

*the*

*method*of tubular neighborhoods used by Gross. {

*For*

*the*entire collection see MR 92c:81004.} ...

*The*paper is

*a*discussion concerning infinite-dimensional

*Sobolev*inequalities and

*logarithmic*

*Sobolev*inequalities.

*For*

*the*finite- dimensional case, see two other papers [L. Gross, Amer. J. ...

##
###
On logarithmic Sobolev inequalities for the heat kernel on the Heisenberg group
[article]

2018
*
arXiv
*
pre-print

In this note, we derive

arXiv:1607.02741v2
fatcat:7ky7kcxsyfd7xpfbuidb37iupq
*a*new*logarithmic**Sobolev*inequality*for**the*heat kernel on*the*Heisenberg group. ...*The*proof is inspired from*the*historical*method*of Leonard Gross with*the*Central Limit Theorem*for**a*random walk. ... Acknowledgements D.C. would like to thank Leonard Gross*for*his encouragement to explore this problem and Fabrice Baudoin*for*his hospitality during*a*visit to Purdue University in Fall 2008. ...##
###
On logarithmic Sobolev inequalities for the heat kernel on the Heisenberg group

2020
*
Annales de la Faculté des Sciences de Toulouse
*

Acknowledgements D.C. would like to thank Leonard Gross

doi:10.5802/afst.1633
fatcat:27ae3lsjhbcmzintmw237pxnqa
*for*his encouragement to explore this problem and Fabrice Baudoin*for*his hospitality during*a*visit to Purdue University in Fall 2008. ... We follow*the**method*developed by Leonard Gross in [12]*for**the*Gaussian and in [13]*for**the**path*space on elliptic Lie groups. ... Li inequality*For*β = 0, Hong-Quan Li has obtained in [17] (see also [1, 10]*for**a*Poincaré inequality)*the*following*logarithmic**Sobolev*inequality: there exists*a**constant*C LSI > 0 such that*for*...##
###
Martingale Representation and a Simple Proof of Logarithmic Sobolev Inequalities on Path Spaces

1997
*
Electronic Communications in Probability
*

By an appropriate integration by parts formula

doi:10.1214/ecp.v2-986
fatcat:ygkx2nvjgnfd5bpzz3z25imh7a
*the*proof also yields in*the*same way*a**logarithmic**Sobolev*inequality*for**the**path*space equipped with*a*general diffusion measure as long as*the*torsion ... Fang in his proof of*the*spectral gap inequality*for**the*Ornstein-Uhlenbeck operator on*the**path*space can yield in*a*very simple way*the**logarithmic**Sobolev*inequality on*the*same space. ... Driver*for*his help at*the*early stage of this work and*for*his suggestion of further developing this approach in*the*case of*a*connection with torsion. ...##
###
Page 559 of Mathematical Reviews Vol. , Issue 2000a
[page]

2000
*
Mathematical Reviews
*

*The*perturbation of

*the*spectral gap and

*the*

*logarithmic*

*Sobolev*

*constant*under

*a*linear transform are given (Theorem 5). ...

*A*new proof

*for*computing

*the*

*logarithmic*

*Sobolev*

*constant*in

*a*basic case is also presented (Theorem 7).” 2000a:60141 60527 60J45 He, Ping (J-KANASN; Kanazawa)

*The*structure of excursions of Markov chains ...

##
###
On the variational interpretation of local logarithmic Sobolev inequalities
[article]

2021
*
arXiv
*
pre-print

inequalities such as

arXiv:2011.05207v3
fatcat:efgn7trdaje7vakbiyos76ihvq
*the**Logarithmic**Sobolev*inequality. ... In this short note we close this gap by explaining how Otto calculus applied to*the*Schrödinger problem yields*a*variations interpretation of*the*local*logarithmic**Sobolev*inequalities, that could possibly ... Acknowledgements This reflexion was supported by*the*French ANR-17-CE40-0030 EFI project. ...##
###
Page 4756 of Mathematical Reviews Vol. , Issue 2004f
[page]

2004
*
Mathematical Reviews
*

These are worked out

*for*some special cases.” 2004f:60017 60C05 Roberto, Cyril (F-TOUL3; Toulouse)*A**path**method**for**the**logarithmic**Sobolev**constant*. (English summary) Combin. Probab. ...*The*author develops*a**path*combinatoric*method*to obtain new bounds on*the**logarithmic**Sobolev**constant*on*a*countable set. He generalizes Sinclair’s bounds [*A*. Sinclair, Combin. Probab. ...##
###
Concentration of measure and logarithmic Sobolev inequalities
[chapter]

1999
*
Lecture notes in mathematics
*

We then discuss some recent

doi:10.1007/bfb0096511
fatcat:hq5vnzqzx5gdlilffh3qa5njom
*logarithmic**Sobolev*inequality*for*Wiener measure on*the**paths*of*a*Riemannian manifold. ... We only aim to show here unity of*the**method*, deriving this large deviation estimate from*logarithmic**Sobolev*inequalities*for*heat kernel measures and Wiener measures on*path*spaces developed recently ...##
###
Logarithmic Sobolev inequalities for harmonic measures on spheres

2014
*
Journal des Mathématiques Pures et Appliquées
*

We study

doi:10.1016/j.matpur.2013.11.008
fatcat:iuvni4v4ajhopbe2njwqqiwbye
*the*corresponding optimal*constants*of*logarithmic**Sobolev*and Poincaré inequalities, denoted respectively by C LS ... In this paper, we consider*the*family of harmonic measures µ n x (indexed by x ∈ R n with |x| < 1) on*the*unit sphere S n−1 in R n ,*for*n ≥ 3. ... We denote by C LS (µ)*the*best*constant*in*the**logarithmic**Sobolev*inequality. ...##
###
Page 4410 of Mathematical Reviews Vol. , Issue 97G
[page]

1997
*
Mathematical Reviews
*

This

*method*is based on use of*the*hypercontractivity property of*the*Markov semigroup or equivalently of*the**logarithmic**Sobolev*inequality*for**the*corresponding generator. ... {*For**the*entire collection see MR 97a:00031.} 97g:60104 60J65 60G17 Brzezniak, Zdzislaw (4-HULL,; Hull) On*Sobolev*and Besov spaces regularity of Brownian*paths*. ...
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