{"id":20820,"date":"2024-12-02T22:15:33","date_gmt":"2024-12-02T21:15:33","guid":{"rendered":"https:\/\/djalil.chafai.net\/blog\/?p=20820"},"modified":"2025-01-07T15:51:44","modified_gmt":"2025-01-07T14:51:44","slug":"logarithmic-sobolev-inequalities-again","status":"publish","type":"post","link":"https:\/\/djalil.chafai.net\/blog\/2024\/12\/02\/logarithmic-sobolev-inequalities-again\/","title":{"rendered":"Logarithmic Sobolev inequalities again..."},"content":{"rendered":"<p><iframe loading=\"lazy\" title=\"Grimes, Bleachers - Entropy (Audio)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/Dt0IiGxNntw?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<p style=\"text-align: justify;\">Unexpectedly, it turned out that this year, I gave twice an introductive mini-course on logarithmic Sobolev inequalities, for distinct audiences, at Institut Henri Poincar\u00e9, in April, and at \u00c9cole normale sup\u00e9rieure, in December. Here are the short notes : <a href=\"https:\/\/djalil.chafai.net\/docs\/chafai-mini-lsi-2024.pdf\">PDF<\/a>.<\/p>\n<p style=\"text-align: justify;\">There is something fun about it. I like very much to connect logarithmic Sobolev inequalities to the work of Boltzmann. This is not what I have learned, since my teachers Dominique Bakry, Michel Ledoux, and Laurent Saloff-Coste were not particularly versed in or attracted by Physics. Meanwhile, C\u00e9dric Villani, who knows very well Boltzmann, is a limited probabilist. Personally, I like very much the Physics of Boltzmann, however, I am not excited and seduced by the technical mathematics that have been constructed around his evolution equation. I have discovered that many of the mathematicians specialists of this equation are not even aware of what is really a Boltzmann-Gibbs measure. All these facts are striking effects of hyperspecialization in science. A somewhat similar phenomenon can be observed for the Schr\u00f6dinger equation, which has a deep probabilistic and physical content, but which is studied by several high profile mathematicians from the mathematical analysis perspective, with often a very limited culture in probability and even in Physics. All this should be seen as a motivation to give more introductory talks, across fields, to reduce the effects of hyperspecialization. At least this is what I try to do !<\/p>\n<p style=\"text-align: justify;\">In a way culture is the result of curiosity and memorization. A limited culture comes from a limited curiosity and\/or memorization. Curiosity is instinctual, takes time, requires effort, and implies a sort of intellectual appetite for danger, since it could force to revisit some foundational certainties. Also it is often replaced by a sort of contempt, hiding an intellectual laziness. These mechanisms can operate at various scales\/scopes, with various intensities, and vary over time.<\/p>\n<p style=\"text-align: justify;\">Even if it can help, a pluridisciplinary culture is neither necessary nor sufficient for being deep and creative, it is something else. Curiosity can be even defocussing, time consuming, and counterproductive in the short-term. This plays into the game of hyperspecialization, which is essentially the result of a sort of short-term utilitarianism, something unconscious which is implicitly encouraged by the selective educational and academic systems. However, an advantage of culture is that it always helps to be a better teacher and guide for young people.<\/p>\n<blockquote><p>Everything I've ever known is wrong<br \/>\nOh, what's the matter with me?<br \/>\nDid I even want it?<br \/>\nDid I just assume that's how it had to be?<\/p>\n<p>Throw a ball, it's bouncing off the wall<br \/>\nThat's how I heard music first<br \/>\nDid I really need it?<br \/>\nHow can something so free feel so rehearsed?<\/p>\n<p>Calculate the entropy<br \/>\nRunning out of energy<br \/>\nA lack of love or empathy<br \/>\nLeave me lonely<br \/>\nCalculate the entropy<br \/>\nBitter path in front of me<br \/>\nOh neither friend or enemy<br \/>\nLeave me lonely<\/p>\n<p>Every day I let the music play<br \/>\nIt seems to play by itself<br \/>\nDid I let it bleed me?<br \/>\nDid I hit it back until it bled itself?<\/p>\n<p>But Daddy I Love Him<br \/>\nTaylor Swift<br \/>\nI Can Do It With a Broken Heart<br \/>\nTaylor Swift<\/p>\n<p>How the birds can sing a tuneless song?<br \/>\nHow can they stay in the sky?<br \/>\nMaybe they're just screaming<br \/>\nMaybe it's not music and it's all a lie<\/p>\n<p>Calculate the entropy<br \/>\nRunning out of energy<br \/>\nA lack of love or empathy<br \/>\nLeave me lonely<br \/>\nCalculate the entropy<br \/>\nBitter path in front of me<br \/>\nOh neither friend or enemy<br \/>\nLeave me lonely<\/p>\n<p>E-eh, e-eh, e-eh, eh<br \/>\nE-e-eh, eh<br \/>\nE-eh, e-eh, e-eh, eh<br \/>\nE-e-eh, eh<\/p>\n<p>Calculate the entropy<br \/>\nRunning out of energy<br \/>\nA lack of love or empathy<br \/>\nLeave me lonely<br \/>\nCalculate the entropy<br \/>\nBitter path in front of me<br \/>\nOh neither friend or enemy<br \/>\nLeave me lonely<\/p>\n<p>Keep me lonely<br \/>\nKeep me lonely<br \/>\nKeep me lonely<br \/>\nKeep me lonely<br \/>\nKeep me lonely<br \/>\nKeep me lonely<br \/>\nKeep me lonely<br \/>\nKeep me lonely<\/p><\/blockquote>\n<p style=\"text-align:justify;\"><strong>PS (December 28, 2024).<\/strong> Leonard Gross, aged 93, who forged the concept of logarithmic Sobolev inequalities in 1973, has just posted on arXiv a <a href=\"https:\/\/arXiv.org\/abs\/2412.20282\">manuscript on the invariance of intrinsic hypercontractivity under perturbation of Schr\u00f6dinger operators<\/a>.\n<\/p>\n<p style=\"text-align:justify;\"><strong>PS (January 1, 2025).<\/strong> C\u00e9dric Villani has just posted on arXiv a <a href=\"https:\/\/arxiv.org\/abs\/2501.00925\">course on Fisher information in kinetic theory<\/a>, in which he makes the effort to start from the maximum likelihood of Ronald Aymler Fisher in Statistics, and in which he uses crucially a logarithmic Sobolev inequality, on the real projective space, for the Boltzmann equation.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Unexpectedly, it turned out that this year, I gave twice an introductive mini-course on logarithmic Sobolev inequalities, for distinct audiences, at Institut Henri Poincar&eacute;, in&#8230;<\/p>\n<div class=\"more-link-wrapper\"><a class=\"more-link\" href=\"https:\/\/djalil.chafai.net\/blog\/2024\/12\/02\/logarithmic-sobolev-inequalities-again\/\">Continue reading<span class=\"screen-reader-text\">Logarithmic Sobolev inequalities again...<\/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":441},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/posts\/20820"}],"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=20820"}],"version-history":[{"count":103,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/posts\/20820\/revisions"}],"predecessor-version":[{"id":21242,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/posts\/20820\/revisions\/21242"}],"wp:attachment":[{"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/media?parent=20820"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/categories?post=20820"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/djalil.chafai.net\/blog\/wp-json\/wp\/v2\/tags?post=20820"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}