{"id":5111,"date":"2019-08-09T18:06:59","date_gmt":"2019-08-09T18:06:59","guid":{"rendered":"https:\/\/artsci.case.edu\/funding\/?p=5111"},"modified":"2019-08-09T18:07:41","modified_gmt":"2019-08-09T18:07:41","slug":"the-random-matrix-theory-of-classical-compact-groups","status":"publish","type":"post","link":"https:\/\/artsci.case.edu\/funding\/the-random-matrix-theory-of-classical-compact-groups\/","title":{"rendered":"The Random Matrix Theory of Classical Compact Groups"},"content":{"rendered":"<p>Elizabeth Meckes, Professor, Department of Mathematics, Applied Mathematics &amp; Statistics (Cambridge University Press). This is the first book to provide a comprehensive overview of foundational results and recent progress in the study of random matrices from the classical compact groups, drawing on the subject&#8217;s deep connections to geometry, analysis, algebra, physics, and statistics. The book sets a foundation with an introduction to the groups themselves and six different constructions of Haar measure. Classical and recent results are then presented in a digested, accessible form, including the following: results on the joint distributions of the entries; an extensive treatment of eigenvalue distributions, including the Weyl integration formula, moment formulae, and limit theorems and large deviations for the spectral measures; concentration of measure with applications both within random matrix theory and in high dimensional geometry; and results on characteristic polynomials with connections to the Riemann zeta function. This book will be a useful reference for researchers and an accessible introduction for students in related fields.<\/p>\n<p>Learn more at <a href=\"https:\/\/www.cambridge.org\/us\/academic\/subjects\/statistics-probability\/probability-theory-and-stochastic-processes\/random-matrix-theory-classical-compact-groups?format=HB&amp;isbn=9781108419529\">Cambridge University Press<\/a><\/p>\n<p>Meckes, Elizabeth.\u00a0<i>The Random Matrix Theory of the Classical\u00a0Compact Group.\u00a0<\/i>Cambridge University Press, 2019.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Elizabeth Meckes, Professor, Department of Mathematics, Applied Mathematics &amp; Statistics (Cambridge University Press). This is the first book to provide a comprehensive overview of foundational results and recent progress in the study of random matrices from the classical compact groups, drawing on the subject&#8217;s deep connections to geometry, analysis, algebra, physics, and statistics. The book sets a foundation with an introduction to the groups themselves and six different constructions of Haar measure. Classical and recent results are then presented in a digested, accessible form, including the following: results on the joint distributions of the entries; an extensive treatment of eigenvalue distributions,<\/p>\n<p><a href=\"https:\/\/artsci.case.edu\/funding\/the-random-matrix-theory-of-classical-compact-groups\/\" class=\"more-link\">Continue reading&#8230; <span class=\"screen-reader-text\">The Random Matrix Theory of Classical Compact Groups<\/span><\/a><\/p>\n","protected":false},"author":19,"featured_media":5112,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[58],"tags":[],"jetpack_featured_media_url":"https:\/\/artscimedia.case.edu\/wp-content\/uploads\/sites\/89\/2019\/08\/09180421\/Meckes-Book-e1565374051992.jpg","_links":{"self":[{"href":"https:\/\/artsci.case.edu\/funding\/wp-json\/wp\/v2\/posts\/5111"}],"collection":[{"href":"https:\/\/artsci.case.edu\/funding\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/artsci.case.edu\/funding\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/artsci.case.edu\/funding\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/artsci.case.edu\/funding\/wp-json\/wp\/v2\/comments?post=5111"}],"version-history":[{"count":1,"href":"https:\/\/artsci.case.edu\/funding\/wp-json\/wp\/v2\/posts\/5111\/revisions"}],"predecessor-version":[{"id":5113,"href":"https:\/\/artsci.case.edu\/funding\/wp-json\/wp\/v2\/posts\/5111\/revisions\/5113"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/artsci.case.edu\/funding\/wp-json\/wp\/v2\/media\/5112"}],"wp:attachment":[{"href":"https:\/\/artsci.case.edu\/funding\/wp-json\/wp\/v2\/media?parent=5111"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/artsci.case.edu\/funding\/wp-json\/wp\/v2\/categories?post=5111"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/artsci.case.edu\/funding\/wp-json\/wp\/v2\/tags?post=5111"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}