{"id":49,"date":"2010-05-21T00:59:10","date_gmt":"2010-05-20T22:59:10","guid":{"rendered":"http:\/\/djalil.chafai.net\/blog\/?p=49"},"modified":"2019-11-10T19:25:19","modified_gmt":"2019-11-10T18:25:19","slug":"gamma-two","status":"publish","type":"post","link":"https:\/\/djalil.chafai.net\/blog\/2010\/05\/21\/gamma-two\/","title":{"rendered":"Gamma two"},"content":{"rendered":"<p style=\"text-align: justify;\">I realized this week that my <a title=\"Michel Ledoux\" href=\"\/scripts\/search.php\/?q=Michel+Ledoux+Mathematics\">former PhD advisor<\/a> has spent a significant amount of his\u00a0 research time juggling with the <a title=\"Majorizing measures: the generic chaining\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=1411488\">Talagrand $\\gamma_2$<\/a> and the <a title=\"Functional inequalities for Markov semigroups\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=2213477\">Bakry-\u00c9mery  $\\Gamma_{\\!\\!2}$<\/a>. He belongs to this very small set of individuals versed in these two universes, between analysis, geometry, and probability. The link is clearly the Gaussian law. It might be amusing to connect the two in a deep statement.<\/p>\n<p style=\"text-align: justify;\">Recently, a kind of <a title=\"Functional inequalities for Markov semigroups\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=2213477\">Bakry-\u00c9mery $\\Gamma_2$<\/a> was developed for <a title=\"Ricci curvature of Markov chains on metric spaces\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=2484937\">Markov chains on metric spaces<\/a>.<\/p>\n<p style=\"text-align: justify;\">More recently, the <a title=\"Majorizing measures: the generic chaining\" href=\"http:\/\/www.ams.org\/mathscinet-getitem?mr=1411488\">Talagrand $\\gamma_2$<\/a> was used successfully for <a title=\"Cover times, blanket times, and majorizing measures\" href=\"http:\/\/arxiv.org\/abs\/1004.4371\">random walks on graphs<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I realized this week that my former PhD advisor has spent a significant amount of his&nbsp; research time juggling with the Talagrand $\\gamma_2$ and the&#8230;<\/p>\n<div class=\"more-link-wrapper\"><a class=\"more-link\" href=\"https:\/\/djalil.chafai.net\/blog\/2010\/05\/21\/gamma-two\/\">Continue reading<span class=\"screen-reader-text\">Gamma two<\/span><\/a><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":47},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/posts\/49"}],"collection":[{"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/comments?post=49"}],"version-history":[{"count":3,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/posts\/49\/revisions"}],"predecessor-version":[{"id":11767,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/posts\/49\/revisions\/11767"}],"wp:attachment":[{"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/media?parent=49"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/categories?post=49"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/tags?post=49"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}