A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Filters
Logarithmic Sobolev, isoperimetry and transport inequalities on graphs
2016
Acta Mathematica Sinica. English series
Preserved Fulltext
We provide estimates of 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 ...
doi:10.1007/s10114-016-5330-9
fatcat:qhzj2rtdw5ez7kal4sf3ol5ogi
Log-Sobolev, isoperimetry and transport inequalities on graphs
[article]
2015
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
and transportation-entropy inequalities) 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. ...
arXiv:1505.04552v1
fatcat:plkovrl7xzhgrdruhwsnw6phwe
Logarithmic Harnack Inequalities
1996
Mathematical Research Letters
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2005; you can also visit the original URL.
The file type is application/pdf.
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. ...
doi:10.4310/mrl.1996.v3.n6.a8
fatcat:s6lp2csc5necdcqisjoh2vzmzq
Page 5069 of Mathematical Reviews Vol. , Issue 97H
[page]
1997
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
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
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2014; you can also visit the original URL.
The file type is application/pdf.
In this paper, we consider 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 . ...
doi:10.1214/ecp.v19-3071
fatcat:xt6jymc27jalbbxt3fc3hbizxa
Page 3262 of Mathematical Reviews Vol. , Issue 93f
[page]
1993
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
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
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
In this note, we derive 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. ...
arXiv:1607.02741v2
fatcat:7ky7kcxsyfd7xpfbuidb37iupq
On logarithmic Sobolev inequalities for the heat kernel on the Heisenberg group
2020
Annales de la Faculté des Sciences de Toulouse
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
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. ...
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 ...
doi:10.5802/afst.1633
fatcat:27ae3lsjhbcmzintmw237pxnqa
Martingale Representation and a Simple Proof of Logarithmic Sobolev Inequalities on Path Spaces
1997
Electronic Communications in Probability
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
By an appropriate integration by parts formula 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. ...
doi:10.1214/ecp.v2-986
fatcat:ygkx2nvjgnfd5bpzz3z25imh7a
Page 559 of Mathematical Reviews Vol. , Issue 2000a
[page]
2000
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
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
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
Other Versions
inequalities such as 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. ...
arXiv:2011.05207v3
fatcat:efgn7trdaje7vakbiyos76ihvq
Page 4756 of Mathematical Reviews Vol. , Issue 2004f
[page]
2004
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
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
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
We then discuss some recent 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 ...
doi:10.1007/bfb0096511
fatcat:hq5vnzqzx5gdlilffh3qa5njom
Logarithmic Sobolev inequalities for harmonic measures on spheres
2014
Journal des Mathématiques Pures et Appliquées
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2014; you can also visit the original URL.
The file type is application/pdf.
We study 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. ...
doi:10.1016/j.matpur.2013.11.008
fatcat:iuvni4v4ajhopbe2njwqqiwbye
Page 4410 of Mathematical Reviews Vol. , Issue 97G
[page]
1997
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
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. ...
« Previous
Showing results 1 — 15 out of 4,159 results