Correlation and Brascamp-Lieb Inequalities for Markov Semigroups

This paper builds upon several recent works, where semigroup proofs of Brascamp-Lieb inequalities are provided in various settings (Euclidean space, spheres, and symmetric groups). Our aim is two-fold. Firstly, we provide a general, unifying, framework based on Markov generators, in order to cover a...

Full description

Saved in:
Bibliographic Details
Published in:International mathematics research notices 2011-01 (10), p.2177-2216
Main Authors: Barthe, F., Cordero-Erausquin, D., Ledoux, M., Maurey, B.
Format: Article
Language:English
Subjects:
Mathematical Physics
Mathematics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c333t-d605d335f7c616a7236c0da3a31ecef5e68a9b00e24281d91c395d3e97daa7b83
cites cdi_FETCH-LOGICAL-c333t-d605d335f7c616a7236c0da3a31ecef5e68a9b00e24281d91c395d3e97daa7b83
container_end_page 2216
container_issue 10
container_start_page 2177
container_title International mathematics research notices
container_volume
creator Barthe, F.
Cordero-Erausquin, D.
Ledoux, M.
Maurey, B.
description This paper builds upon several recent works, where semigroup proofs of Brascamp-Lieb inequalities are provided in various settings (Euclidean space, spheres, and symmetric groups). Our aim is two-fold. Firstly, we provide a general, unifying, framework based on Markov generators, in order to cover a variety of examples of interest going beyond previous investigations. Secondly, we put forward the combinatorial reasons for which unexpected exponents occur in these inequalities. Related superadditivity of information and entropy inequalities are also studied.
doi_str_mv 10.1093/imrn/rnq114
format article
fullrecord <record><control><sourceid>hal_cross</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_00693000v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>oai_HAL_hal_00693000v1</sourcerecordid><originalsourceid>FETCH-LOGICAL-c333t-d605d335f7c616a7236c0da3a31ecef5e68a9b00e24281d91c395d3e97daa7b83</originalsourceid><addsrcrecordid>eNo9kDFPwzAUhC0EEqUw8QeyIhT6nNfa8UapCq0UxADM1ovjgCGJUzutxL-nVRHTnU53N3yMXXO446Bw4trQTUK34Xx6wkZc5DKFbCpP9x4kplJl-Tm7iPELIAOe44jdL3wItqHB-S6hrkoeAkVDbZ8WzpbJurObLTVucDYmtQ_JM4Vvv0tebes-gt_28ZKd1dREe_WnY_b-uHxbrNLi5Wm9mBepQcQhrQTMKsRZLY3ggmSGwkBFSMitsfXMipxUCWCzaZbzSnGDaj-wSlZEssxxzG6Ov5_U6D64lsKP9uT0al7oQwYgFALAju-7t8euCT7GYOv_AQd9AKUPoPQRFP4CcnBcvg</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Correlation and Brascamp-Lieb Inequalities for Markov Semigroups</title><source>Oxford Journals Online</source><creator>Barthe, F. ; Cordero-Erausquin, D. ; Ledoux, M. ; Maurey, B.</creator><creatorcontrib>Barthe, F. ; Cordero-Erausquin, D. ; Ledoux, M. ; Maurey, B.</creatorcontrib><description>This paper builds upon several recent works, where semigroup proofs of Brascamp-Lieb inequalities are provided in various settings (Euclidean space, spheres, and symmetric groups). Our aim is two-fold. Firstly, we provide a general, unifying, framework based on Markov generators, in order to cover a variety of examples of interest going beyond previous investigations. Secondly, we put forward the combinatorial reasons for which unexpected exponents occur in these inequalities. Related superadditivity of information and entropy inequalities are also studied.</description><identifier>ISSN: 1073-7928</identifier><identifier>EISSN: 1687-0247</identifier><identifier>DOI: 10.1093/imrn/rnq114</identifier><language>eng</language><publisher>Oxford University Press (OUP)</publisher><subject>Mathematical Physics ; Mathematics</subject><ispartof>International mathematics research notices, 2011-01 (10), p.2177-2216</ispartof><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c333t-d605d335f7c616a7236c0da3a31ecef5e68a9b00e24281d91c395d3e97daa7b83</citedby><cites>FETCH-LOGICAL-c333t-d605d335f7c616a7236c0da3a31ecef5e68a9b00e24281d91c395d3e97daa7b83</cites><orcidid>0000-0003-0104-0816</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,777,781,882,27905,27906</link.rule.ids><backlink>$$Uhttps://hal.science/hal-00693000$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Barthe, F.</creatorcontrib><creatorcontrib>Cordero-Erausquin, D.</creatorcontrib><creatorcontrib>Ledoux, M.</creatorcontrib><creatorcontrib>Maurey, B.</creatorcontrib><title>Correlation and Brascamp-Lieb Inequalities for Markov Semigroups</title><title>International mathematics research notices</title><description>This paper builds upon several recent works, where semigroup proofs of Brascamp-Lieb inequalities are provided in various settings (Euclidean space, spheres, and symmetric groups). Our aim is two-fold. Firstly, we provide a general, unifying, framework based on Markov generators, in order to cover a variety of examples of interest going beyond previous investigations. Secondly, we put forward the combinatorial reasons for which unexpected exponents occur in these inequalities. Related superadditivity of information and entropy inequalities are also studied.</description><subject>Mathematical Physics</subject><subject>Mathematics</subject><issn>1073-7928</issn><issn>1687-0247</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNo9kDFPwzAUhC0EEqUw8QeyIhT6nNfa8UapCq0UxADM1ovjgCGJUzutxL-nVRHTnU53N3yMXXO446Bw4trQTUK34Xx6wkZc5DKFbCpP9x4kplJl-Tm7iPELIAOe44jdL3wItqHB-S6hrkoeAkVDbZ8WzpbJurObLTVucDYmtQ_JM4Vvv0tebes-gt_28ZKd1dREe_WnY_b-uHxbrNLi5Wm9mBepQcQhrQTMKsRZLY3ggmSGwkBFSMitsfXMipxUCWCzaZbzSnGDaj-wSlZEssxxzG6Ov5_U6D64lsKP9uT0al7oQwYgFALAju-7t8euCT7GYOv_AQd9AKUPoPQRFP4CcnBcvg</recordid><startdate>20110101</startdate><enddate>20110101</enddate><creator>Barthe, F.</creator><creator>Cordero-Erausquin, D.</creator><creator>Ledoux, M.</creator><creator>Maurey, B.</creator><general>Oxford University Press (OUP)</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0003-0104-0816</orcidid></search><sort><creationdate>20110101</creationdate><title>Correlation and Brascamp-Lieb Inequalities for Markov Semigroups</title><author>Barthe, F. ; Cordero-Erausquin, D. ; Ledoux, M. ; Maurey, B.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c333t-d605d335f7c616a7236c0da3a31ecef5e68a9b00e24281d91c395d3e97daa7b83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Mathematical Physics</topic><topic>Mathematics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Barthe, F.</creatorcontrib><creatorcontrib>Cordero-Erausquin, D.</creatorcontrib><creatorcontrib>Ledoux, M.</creatorcontrib><creatorcontrib>Maurey, B.</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>International mathematics research notices</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Barthe, F.</au><au>Cordero-Erausquin, D.</au><au>Ledoux, M.</au><au>Maurey, B.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Correlation and Brascamp-Lieb Inequalities for Markov Semigroups</atitle><jtitle>International mathematics research notices</jtitle><date>2011-01-01</date><risdate>2011</risdate><issue>10</issue><spage>2177</spage><epage>2216</epage><pages>2177-2216</pages><issn>1073-7928</issn><eissn>1687-0247</eissn><abstract>This paper builds upon several recent works, where semigroup proofs of Brascamp-Lieb inequalities are provided in various settings (Euclidean space, spheres, and symmetric groups). Our aim is two-fold. Firstly, we provide a general, unifying, framework based on Markov generators, in order to cover a variety of examples of interest going beyond previous investigations. Secondly, we put forward the combinatorial reasons for which unexpected exponents occur in these inequalities. Related superadditivity of information and entropy inequalities are also studied.</abstract><pub>Oxford University Press (OUP)</pub><doi>10.1093/imrn/rnq114</doi><tpages>40</tpages><orcidid>https://orcid.org/0000-0003-0104-0816</orcidid></addata></record>
fulltext fulltext
identifier ISSN: 1073-7928
ispartof International mathematics research notices, 2011-01 (10), p.2177-2216
issn 1073-7928
1687-0247
language eng
recordid cdi_hal_primary_oai_HAL_hal_00693000v1
source Oxford Journals Online
subjects Mathematical Physics
Mathematics
title Correlation and Brascamp-Lieb Inequalities for Markov Semigroups
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-20T05%3A19%3A46IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-hal_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Correlation%20and%20Brascamp-Lieb%20Inequalities%20for%20Markov%20Semigroups&rft.jtitle=International%20mathematics%20research%20notices&rft.au=Barthe,%20F.&rft.date=2011-01-01&rft.issue=10&rft.spage=2177&rft.epage=2216&rft.pages=2177-2216&rft.issn=1073-7928&rft.eissn=1687-0247&rft_id=info:doi/10.1093/imrn/rnq114&rft_dat=%3Chal_cross%3Eoai_HAL_hal_00693000v1%3C/hal_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c333t-d605d335f7c616a7236c0da3a31ecef5e68a9b00e24281d91c395d3e97daa7b83%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true