{"id":17440,"date":"2023-07-24T11:34:19","date_gmt":"2023-07-24T02:34:19","guid":{"rendered":"https:\/\/www.waseda.jp\/fsci\/mathphys\/?p=17440"},"modified":"2023-12-11T13:04:10","modified_gmt":"2023-12-11T04:04:10","slug":"stochastic-processes-in-random-media-special-lectures-3","status":"publish","type":"post","link":"https:\/\/www.waseda.jp\/fsci\/mathphys\/news-en\/17440","title":{"rendered":"Special Lectures &#8220;Gaussian free fields and related topics&#8221;"},"content":{"rendered":"<p>On September 26th and 27th, 2023, the following special lectures will be delivered as part of the international activities of the Multiscale Analysis, Modelling and Simulation Unit. Professor Ofer Zeitouni and Professor Yoshihiro Abe will deliver lectures on Gaussian free fields and related topics.<\/p>\n<h3>Title<\/h3>\n<p>Gaussian free fields and related topics (Special Lectures)<\/p>\n<h3>Dates (Japan Time)<\/h3>\n<h5 class=\"moz-quote-pre\">September 26 (Tuesday)<\/h5>\n<ul>\n<li>14:30-16:10\u00a0\u00a0 Yoshihiro Abe\uff08Mathematical Institute, Tohoku University, Associate Professor \uff09<\/li>\n<li>16:30-18:30\u00a0\u00a0 Ofer Zeitouni (Weizmann Institute of Science and New York University, Professor)<\/li>\n<\/ul>\n<h5 class=\"moz-quote-pre\">September 27 (Wednesday)<\/h5>\n<ul>\n<li>14:30-16:10\u00a0\u00a0 Yoshihiro Abe\uff08Mathematical Institute, Tohoku University, Associate Professor \uff09<\/li>\n<li>16:30-18:30\u00a0\u00a0 Ofer Zeitouni (Weizmann Institute of Science and New York University, Professor)<\/li>\n<\/ul>\n<h3>Lecturer<\/h3>\n<div class=\"table-wrapper\"><table border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 204px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-17430\" src=\"https:\/\/www.waseda.jp\/fsci\/mathphys\/assets\/uploads\/2023\/07\/Photo_Zeitouni-610x697.jpg\" alt=\"\" width=\"610\" height=\"697\" srcset=\"https:\/\/www.waseda.jp\/fsci\/mathphys\/assets\/uploads\/2023\/07\/Photo_Zeitouni-610x697.jpg 610w, https:\/\/www.waseda.jp\/fsci\/mathphys\/assets\/uploads\/2023\/07\/Photo_Zeitouni-940x1074.jpg 940w, https:\/\/www.waseda.jp\/fsci\/mathphys\/assets\/uploads\/2023\/07\/Photo_Zeitouni-768x877.jpg 768w, https:\/\/www.waseda.jp\/fsci\/mathphys\/assets\/uploads\/2023\/07\/Photo_Zeitouni.jpg 1200w\" sizes=\"auto, (max-width: 610px) 100vw, 610px\" \/><\/td>\n<td style=\"width: 679px;\">\n<h6><strong><a href=\"https:\/\/www.wisdom.weizmann.ac.il\/~zeitouni\/\" target=\"_blank\" rel=\"noopener\">Prof. Ofer Zeitouni<\/a><\/strong><\/h6>\n<p>Weizmann Institute of Science and New York University, Professor<\/p>\n<p><span class=\"VIiyi\" lang=\"en\"><span class=\"JLqJ4b ChMk0b\" data-language-for-alternatives=\"en\" data-language-to-translate-into=\"ja\" data-phrase-index=\"0\" data-number-of-phrases=\"1\"><span class=\"Q4iAWc\">Lecture theme:\u00a0\u00a0\u00a0<\/span><\/span><\/span>Extreme value theory for 2D Gaussian free field and\u00a0 logarithmically correlated fields<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 204px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-17429\" src=\"https:\/\/www.waseda.jp\/fsci\/mathphys\/assets\/uploads\/2023\/07\/Photo_Abe-610x698.jpg\" alt=\"\" width=\"610\" height=\"698\" srcset=\"https:\/\/www.waseda.jp\/fsci\/mathphys\/assets\/uploads\/2023\/07\/Photo_Abe-610x698.jpg 610w, https:\/\/www.waseda.jp\/fsci\/mathphys\/assets\/uploads\/2023\/07\/Photo_Abe-940x1076.jpg 940w, https:\/\/www.waseda.jp\/fsci\/mathphys\/assets\/uploads\/2023\/07\/Photo_Abe-768x879.jpg 768w, https:\/\/www.waseda.jp\/fsci\/mathphys\/assets\/uploads\/2023\/07\/Photo_Abe.jpg 1200w\" sizes=\"auto, (max-width: 610px) 100vw, 610px\" \/><\/td>\n<td style=\"width: 679px;\">\n<h6><a href=\"https:\/\/researchmap.jp\/yoshi-abe?lang=en\" target=\"_blank\" rel=\"noopener\">Prof. Yoshihiro Abe<\/a><\/h6>\n<p><a href=\"http:\/\/www.math.tohoku.ac.jp\/english\/people\/abe-e.html\" target=\"_blank\" rel=\"noopener\">Mathematical Institute, Tohoku University, Associate Professor<\/a><\/p>\n<p><span class=\"VIiyi\" lang=\"en\"><span class=\"JLqJ4b ChMk0b\" data-language-for-alternatives=\"en\" data-language-to-translate-into=\"ja\" data-phrase-index=\"0\" data-number-of-phrases=\"1\"><span class=\"Q4iAWc\">Lecture theme:\u00a0\u00a0\u00a0<\/span><\/span><\/span>Discrete Gaussian free fields and its applications to random walks<\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>\n<h3>Venue<\/h3>\n<p>Room 205, 2nd Floor, Building 63, Waseda University, Nishi-Waseda Campus (<a href=\"https:\/\/www.waseda.jp\/top\/en\/access\/nishiwaseda-campus\" target=\"_blank\" rel=\"noopener\">Access<\/a>)\/ Online via Zoom<\/p>\n<h3>Language<\/h3>\n<p>English<\/p>\n<h3>Audience<\/h3>\n<p>Researchers, Students<br \/>\nOpen to the public through Zoom<\/p>\n<h3>Registration<\/h3>\n<p>Required. Please register from<a href=\"https:\/\/forms.gle\/i4zugLz4X1Vi15HU8\" target=\"_blank\" rel=\"noopener\"> here.<\/a><\/p>\n<h3 class=\"moz-quote-pre\">Contact information<\/h3>\n<h5>Inquiries about lecture content<\/h5>\n<p>Takashi KUMAGAI\u00a0 (Professor, Faculty of Science and Engineering, Waseda University)<br \/>\nt-kumagai [at] waseda.jp<\/p>\n<h5>Inquiries about registration, etc.<\/h5>\n<p>Multiscale Analysis, Modelling and Simulation Unit<br \/>\ninfo [at] sgu-mathphys.sci.waseda.ac.jp<\/p>\n<h3>Time Table\u3000(Including Q&amp;A time)<\/h3>\n<h4>September 26 (Tuesday), Japan Time<\/h4>\n<div class=\"table-wrapper\"><table style=\"width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 8.35215%;\">\n<h6>14:30 &#8211; 16:10<\/h6>\n<\/td>\n<td style=\"width: 90.0677%;\">\n<h5>Yoshihiro Abe\uff08Mathematical Institute, Tohoku University, Associate Professor \uff09<br \/>\n&#8220;Introduction to the discrete Gaussian free field&#8221;<\/h5>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 8.35215%;\"><\/td>\n<td style=\"width: 90.0677%;\">(Abstract)<br \/>\nThe discrete Gaussian free field (DGFF) is a centered Gaussian field on a graph whose covariance is given by the inverse of the graph Laplacian. It is a probabilistic model of interfaces and has connections with a lot of other models such as local times of random walks and branching random walks. In the first half of this lecture, I will give some motivation and basics of DGFF such as the random walk representation and the domain Markov property. In the second half, I will review some progress on the extreme value theory of DGFF on the integer lattice in three or higher dimensions.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 8.35215%;\">\n<h6>16:30 &#8211; 18:30<\/h6>\n<\/td>\n<td style=\"width: 90.0677%;\">\n<h5>Ofer Zeitouni (Weizmann Institute of Science and New York University, Professor)<br \/>\n&#8220;Extreme value theory for Gaussian logarithmically correlated fields&#8221;<\/h5>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 8.35215%;\"><\/td>\n<td style=\"width: 90.0677%;\">(Abstract)<br \/>\nThe extreme value theory for Gaussian logarithmically correlated fields (G-LCFs) has emerged in the last decade as a powerful tool in the analysis of interface models, quantum gravity, random matrices and in a myriad of other applications.<br \/>\nThe two dimensional Gaussian free field (and its discrete analogue) is an important motivating\u00a0 example of such a field. In this lecture, I will describe the relation and differences between the extreme value theory for i.i.d. variables and that for G.-LCFs, and introduce the relation with branching structures and various tools such as comparison theorems, scale decompositions and relations to branching random walks.<\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>\n<h4>September 27 (Wednesday), Japan Time<\/h4>\n<div class=\"table-wrapper\"><table border=\"0\">\n<tbody>\n<tr>\n<td>\n<h6>14:30 &#8211; 16:10<\/h6>\n<\/td>\n<td>\n<h5>Yoshihiro Abe\uff08Mathematical Institute, Tohoku University, Associate Professor \uff09<br \/>\n&#8220;Applications of the discrete Gaussian free field to random walks&#8221;<\/h5>\n<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>(Abstract)<br \/>\nThe discrete Gaussian free field (DGFF) and the simple random walk (SRW) have a close relationship via the generalized second Ray-Knight theorem, which is a distributional identity between the square of DGFF and the local time of SRW. Thanks to the theorem, we have witnessed rapid progress on the studies of the cover time (the first time at which SRW visits all the vertices) and thick points of SRW (sites frequently visited by SRW). In the first half of this lecture, I will state the generalized second Ray-Knight theorem and review results on the cover time due to Ding-Lee-Peres (2012) and Zhai (2018) where we can see beautiful applications of the theorem. In the second half, I will focus on applications to thick points of SRW.<\/td>\n<\/tr>\n<tr>\n<td>\n<h6>16:30 &#8211; 18:30<\/h6>\n<\/td>\n<td>\n<h5>Ofer Zeitouni (Weizmann Institute of Science and New York University, Professor)<br \/>\n&#8220;Extreme value theory for non-Gaussian logarithmically correlated fields&#8221;<\/h5>\n<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>(Abstract)<br \/>\nIn the first lecture we discussed extreme value theory for logarithmically correlated Gaussian fields. In this talk I will discuss what changes in the non-Gaussian Gaussian setup. A prime example is the study of cover time of certain planar graphs or two dimensional manifolds by random walk or Brownian motion. In spite of precise and beautiful links through isomorphism theorems, the question about the cover time of the 2D torus by a Wiener sausage (or its discrete analogue) requires new tools. I will describe some work, old and recent, on this question, culminating with limit theorems for the cover time.\u00a0 If time permits, I will briefly discuss other types of non Gaussian LCFs.<\/td>\n<\/tr>\n<\/tbody>\n<\/table><\/div>\n<p>&nbsp;<\/p>\n<p><a href=\"https:\/\/www.waseda.jp\/fsci\/mathphys\/assets\/uploads\/2023\/07\/Poster_lecture202309.jpg\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-17479\" src=\"https:\/\/www.waseda.jp\/fsci\/mathphys\/assets\/uploads\/2023\/07\/Poster_lecture202309-610x863.jpg\" alt=\"\" width=\"305\" height=\"431\" srcset=\"https:\/\/www.waseda.jp\/fsci\/mathphys\/assets\/uploads\/2023\/07\/Poster_lecture202309-610x863.jpg 610w, https:\/\/www.waseda.jp\/fsci\/mathphys\/assets\/uploads\/2023\/07\/Poster_lecture202309.jpg 673w\" sizes=\"auto, (max-width: 305px) 100vw, 305px\" \/><\/a><\/p>\n<ul>\n<li><a href=\"https:\/\/www.waseda.jp\/fsci\/mathphys\/assets\/uploads\/2023\/07\/Poster_lecture202309.pdf\" target=\"_blank\" rel=\"noopener\">Poster<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>On September 26th and 27th, 2023, the following special lectures will be delivered as part of the internationa [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":17467,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[18],"tags":[126,83,142],"class_list":["post-17440","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-news-en","tag-education-en","tag-events-en","tag-lecture-en"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/posts\/17440","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/comments?post=17440"}],"version-history":[{"count":2,"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/posts\/17440\/revisions"}],"predecessor-version":[{"id":18623,"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/posts\/17440\/revisions\/18623"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/media\/17467"}],"wp:attachment":[{"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/media?parent=17440"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/categories?post=17440"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.waseda.jp\/fsci\/mathphys\/wp-json\/wp\/v2\/tags?post=17440"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}