{"id":28112,"date":"2024-03-05T07:53:47","date_gmt":"2024-03-05T08:53:47","guid":{"rendered":"https:\/\/express24.ir\/d\/product\/%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%af%d8%b1-%d9%85%d9%88%d8%b1%d8%af-%d8%ad%d8%af%d8%a7%da%a9%d8%ab%d8%b1-%d9%be%d8%aa%d8%a7%d9%86%d8%b3%db%8c%d9%84-%db%8c%da%a9-%da%af%d8%a7%d8%b2-%da%a9%d9%88%d9%84\/"},"modified":"2024-03-05T07:53:48","modified_gmt":"2024-03-05T08:53:48","slug":"%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%af%d8%b1-%d9%85%d9%88%d8%b1%d8%af-%d8%ad%d8%af%d8%a7%da%a9%d8%ab%d8%b1-%d9%be%d8%aa%d8%a7%d9%86%d8%b3%db%8c%d9%84-%db%8c%da%a9-%da%af%d8%a7%d8%b2-%da%a9%d9%88%d9%84","status":"publish","type":"product","link":"https:\/\/express24.ir\/d\/product\/%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%af%d8%b1-%d9%85%d9%88%d8%b1%d8%af-%d8%ad%d8%af%d8%a7%da%a9%d8%ab%d8%b1-%d9%be%d8%aa%d8%a7%d9%86%d8%b3%db%8c%d9%84-%db%8c%da%a9-%da%af%d8%a7%d8%b2-%da%a9%d9%88%d9%84\/","title":{"rendered":"\u0645\u0642\u0627\u0644\u0647 \u062f\u0631 \u0645\u0648\u0631\u062f \u062d\u062f\u0627\u06a9\u062b\u0631 \u067e\u062a\u0627\u0646\u0633\u06cc\u0644 \u06cc\u06a9 \u06af\u0627\u0632 \u06a9\u0648\u0644\u0646 \u062f\u0648 \u0628\u0639\u062f\u06cc \u0639\u0645\u0648\u0645\u06cc"},"content":{"rendered":"<table class=\"table table-striped table-hover\">\n<tbody>\n<tr>\n<td>\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\n<td>On the Maximum of the Potential of a General Two-Dimensional Coulomb Gas<\/td>\n<\/tr>\n<tr>\n<td>\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n<td>\u0645\u0642\u0627\u0644\u0647 \u062f\u0631 \u062d\u062f\u0627\u06a9\u062b\u0631 \u067e\u062a\u0627\u0646\u0633\u06cc\u0644 \u06cc\u06a9 \u06af\u0627\u0632 \u06a9\u0648\u0644\u0648\u0645 \u062f\u0648 \u0628\u0639\u062f\u06cc \u0639\u0645\u0648\u0645\u06cc<\/td>\n<\/tr>\n<tr>\n<td>\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\n<td>Luke Peilen<\/td>\n<\/tr>\n<tr>\n<td>\u0632\u0628\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 <\/td>\n<td>\u0627\u0646\u06af\u0644\u06cc\u0633\u06cc<\/td>\n<\/tr>\n<tr>\n<td>\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647: <\/td>\n<td>PDF<\/td>\n<\/tr>\n<tr>\n<td>\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n<td>17<\/td>\n<\/tr>\n<tr>\n<td>\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0648\u0636\u0648\u0639\u0627\u062a  <\/td>\n<td>Probability,Mathematical Physics,\u0627\u062d\u062a\u0645\u0627\u0644 , \u0641\u06cc\u0632\u06cc\u06a9 \u0631\u06cc\u0627\u0636\u06cc ,<\/td>\n<\/tr>\n<tr>\n<td>\u062a\u0648\u0636\u06cc\u062d\u0627\u062a    <\/td>\n<td>Submitted 1 March, 2024; originally announced March 2024. , Comments: 17 pages<\/td>\n<\/tr>\n<tr>\n<td>\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc    <\/td>\n<td>\u0627\u0631\u0633\u0627\u0644 1 \u0645\u0627\u0631\u0633 2024 \u061b\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0645\u0627\u0631\u0633 2024 \u0627\u0639\u0644\u0627\u0645 \u0634\u062f \u060c \u0646\u0638\u0631\u0627\u062a: 17 \u0635\u0641\u062d\u0647<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u0686\u06a9\u06cc\u062f\u0647<\/h2>\n<p style=\"direction:ltr;\">We determine the leading order of the maximum of the random potential associated to a two-dimensional Coulomb gas for general $\u03b2$ and general confinement potential, extending the recent result of Lambert-Lebl\u00e9-Zeitouni. In the case $\u03b2=2$, this corresponds to the (centered) log-characteristic polynomial of either the Ginibre random matrix ensemble for $V(x)=\\frac{|x|^2}{2}$ or a more general normal matrix ensemble. The result on the leading order asymptotics for the maximum of the log-characteristic polynomial is new for random normal matrices. We rely on connections with the classical obstacle problem and the theory of Gaussian Multiplicative Chaos. We make use of a new concentration result for fluctuations of $C^{1,1}$ linear statistics which may be of independent interest.<\/p>\n<h2>\u0686\u06a9\u06cc\u062f\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc (\u062a\u0631\u062c\u0645\u0647 \u0645\u0627\u0634\u06cc\u0646\u06cc)<\/h2>\n<p>\u0645\u0627 \u062a\u0631\u062a\u06cc\u0628 \u067e\u06cc\u0634\u0631\u0648 \u062d\u062f\u0627\u06a9\u062b\u0631 \u067e\u062a\u0627\u0646\u0633\u06cc\u0644 \u062a\u0635\u0627\u062f\u0641\u06cc \u0645\u0631\u062a\u0628\u0637 \u0628\u0627 \u06cc\u06a9 \u06af\u0627\u0632 \u06a9\u0648\u0644\u0648\u0645 \u062f\u0648 \u0628\u0639\u062f\u06cc \u0631\u0627 \u0628\u0631\u0627\u06cc \u067e\u062a\u0627\u0646\u0633\u06cc\u0644 \u0628\u0632\u0631\u06af \u03b2 \u03b2 $ $ \u0648 \u0639\u0645\u0648\u0645 \u062a\u0639\u06cc\u06cc\u0646 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0648 \u0646\u062a\u06cc\u062c\u0647 \u0627\u062e\u06cc\u0631 \u0644\u0627\u0645\u0628\u0631\u062a-\u0644\u0648\u0628\u0644-\u0632\u06cc\u062a\u0648\u0646\u06cc \u0631\u0627 \u06af\u0633\u062a\u0631\u0634 \u0645\u06cc \u062f\u0647\u06cc\u0645.\u062f\u0631 \u0645\u0648\u0631\u062f $ \u03b2 = 2 $ \u060c \u0627\u06cc\u0646 \u0645\u0631\u0628\u0648\u0637 \u0628\u0647 \u0686\u0646\u062f \u062c\u0645\u0644\u0647 \u0627\u06cc \u0628\u0627\u06a9\u062a\u0631\u06cc\u06a9 \u0644\u0627\u06af (\u0645\u062d\u0648\u0631) \u0627\u0632 \u06af\u0631\u0648\u0647 \u0645\u0627\u062a\u0631\u06cc\u0633 \u062a\u0635\u0627\u062f\u0641\u06cc \u062c\u06cc\u0646\u0628\u0631 \u0628\u0631\u0627\u06cc $ v (x) = \\ frac {| x |^2} {2} $ \u06cc\u0627 \u0628\u06cc\u0634\u062a\u0631 \u0627\u0633\u062a.\u06af\u0631\u0648\u0647 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0639\u0627\u062f\u06cc \u0639\u0645\u0648\u0645\u06cc.\u0646\u062a\u06cc\u062c\u0647 \u062f\u0631 \u0628\u062f\u0648\u0646 \u0639\u0644\u0627\u0645\u062a \u0633\u0641\u0627\u0631\u0634 \u067e\u06cc\u0634\u0631\u0648 \u0628\u0631\u0627\u06cc \u062d\u062f\u0627\u06a9\u062b\u0631 \u0686\u0646\u062f \u0642\u0637\u0628\u06cc \u0628\u0627 \u0645\u0634\u062e\u0635\u0647 \u0648\u0631\u0648\u062f \u0628\u0647 \u0633\u06cc\u0633\u062a\u0645 \u0628\u0631\u0627\u06cc \u0645\u0627\u062a\u0631\u06cc\u0633 \u0647\u0627\u06cc \u0639\u0627\u062f\u06cc \u062a\u0635\u0627\u062f\u0641\u06cc \u062c\u062f\u06cc\u062f \u0627\u0633\u062a.\u0645\u0627 \u0628\u0647 \u0627\u0631\u062a\u0628\u0627\u0637 \u0628\u0627 \u0645\u0634\u06a9\u0644 \u0645\u0627\u0646\u0639 \u06a9\u0644\u0627\u0633\u06cc\u06a9 \u0648 \u0646\u0638\u0631\u06cc\u0647 \u0647\u0631\u062c \u0648 \u0645\u0631\u062c \u0686\u0646\u062f \u0628\u0631\u0627\u0628\u0631 \u06af\u0627\u0648\u0633\u06cc \u0645\u062a\u06a9\u06cc \u0647\u0633\u062a\u06cc\u0645.\u0645\u0627 \u0627\u0632 \u06cc\u06a9 \u0646\u062a\u06cc\u062c\u0647 \u063a\u0644\u0638\u062a \u062c\u062f\u06cc\u062f \u0628\u0631\u0627\u06cc \u0646\u0648\u0633\u0627\u0646\u0627\u062a \u0622\u0645\u0627\u0631 \u062e\u0637\u06cc $ C^{1\u060c1} $ \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0645\u0648\u0631\u062f \u0639\u0644\u0627\u0642\u0647 \u0645\u0633\u062a\u0642\u0644 \u0628\u0627\u0634\u062f.<\/p>\n<table class=\"table table-bordered table-primary\">\r\n<tr>\r\n\t<td>\r\n\t\u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0632\u0628\u0627\u0646 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc \u0627\u0633\u062a.\r\n\t<\/td>\r\n<\/tr>\r\n\t\r\n<tr>\r\n\t<td>\r\n     \u0628\u0631\u0627\u06cc \u0633\u0641\u0627\u0631\u0634 \u062a\u0631\u062c\u0645\u0647 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0628\u0647 \u06cc\u06a9\u06cc \u0627\u0632 \u0631\u0648\u0634 \u0647\u0627\u06cc \u062a\u0645\u0627\u0633\u060c \u067e\u06cc\u0627\u0645\u06a9\u060c \u062a\u0644\u06af\u0631\u0627\u0645 \u0648 \u06cc\u0627 \u0648\u0627\u062a\u0633 \u0627\u067e \u0628\u0627 \u0634\u0645\u0627\u0631\u0647 \u0632\u06cc\u0631 \u062a\u0645\u0627\u0633 \u0628\u06af\u06cc\u0631\u06cc\u062f:\r\n\t<br \/><br \/>\r\n\t09395106248\r\n\t\t\r\n\t\t\r\n\t<br \/><br \/>\r\n\t\t\u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0634\u0631\u0627\u06cc\u0637 \u062a\u0631\u062c\u0645\u0647 \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0627\u0633\u062a:\r\n\t\t<br \/>\r\n\t\t<ul>\r\n\t\t<li>\r\n\t\t\u0642\u06cc\u0645\u062a \u0647\u0631 \u0635\u0641\u062d\u0647 \u062a\u0631\u062c\u0645\u0647 \u062f\u0631 \u062d\u0627\u0644 \u062d\u0627\u0636\u0631 40 \u0647\u0632\u0627\u0631 \u062a\u0648\u0645\u0627\u0646 \u0645\u06cc \u0628\u0627\u0634\u062f. \r\n\t\t<\/li>\r\n\t\t<li>\r\n\t\t\u062a\u062d\u0648\u06cc\u0644 \u0645\u0642\u0627\u0644\u0647 \u062a\u0631\u062c\u0645\u0647 \u0634\u062f\u0647 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f \u0645\u06cc \u0628\u0627\u0634\u062f.\r\n\t\t<\/li>\r\n\t\t<li>\r\n\t\t\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 \u062f\u0631 \u0635\u0648\u0631\u062a \u062f\u0627\u0634\u062a\u0646 \u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a \u0639\u0627\u062f\u06cc \u0628\u06cc\u0646 3 \u062a\u0627 5 \u0631\u0648\u0632 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.\r\n\t\t<\/li>\r\n\t\t\r\n\t\t<li>\r\n\t\t\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627 \u0645\u06cc \u0628\u0627\u0634\u062f. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.\r\n\t\t<\/li>\r\n\t\t<li>\r\n\t\t\u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.\r\n\t\t<\/li>\r\n\t<\/td>\r\n\t\r\n\t\r\n<\/tr>\r\n<\/table>\r\n\r\n\r\n\n","protected":false},"excerpt":{"rendered":"<p>\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc On the Maximum of the Potential of a General Two-Dimensional Coulomb Gas \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc [&hellip;]<\/p>\n","protected":false},"featured_media":27,"comment_status":"open","ping_status":"closed","template":"","meta":{"pmpro_default_level":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center 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