{"id":996,"date":"2014-09-25T14:28:04","date_gmt":"2014-09-25T12:28:04","guid":{"rendered":"https:\/\/webs.uab.cat\/giq\/seminar\/universal-covariance-formula-linear-statistics-random-matrices\/"},"modified":"2014-09-25T14:28:04","modified_gmt":"2014-09-25T12:28:04","slug":"universal-covariance-formula-linear-statistics-random-matrices","status":"publish","type":"seminar","link":"https:\/\/webs.uab.cat\/giq\/seminar\/universal-covariance-formula-linear-statistics-random-matrices\/","title":{"rendered":"Universal Covariance Formula for Linear Statistics on Random Matrices"},"content":{"rendered":"<p><span>Eigenvalues of random matrices provide a prominent example of strongly correlated random variables.&nbsp;<\/span><span>The issue of fluctuations of linear statistics on random matrices (sum functions of the eigenvalues)&nbsp;<\/span><span>has a long history in the physics and mathematics literature.<\/span><br \/><span>After a pedagogical introduction, I will present a recent universal covariance formula for large dimensional random matrices.&nbsp;<\/span><span>I will provide some applications &#8211; asymptotic decorrelation for traces of powers of random matrices,&nbsp;<\/span><span>the joint statistics of conductance and shot noise in ideal chaotic cavities,&nbsp;<\/span><span>and the joint distribution of local Renyi&#8217;s entropies of random quantum states.<\/span><\/p>\n<p><span>For more details see<\/span><br \/><a href=\"http:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.113.070202\" target=\"_blank\" rel=\"noopener\">http:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.113.070202<\/a><br \/><span>or on the arXiv:<\/span><br \/><a href=\"http:\/\/arxiv.org\/abs\/1405.4763\" target=\"_blank\" rel=\"noopener\">http:\/\/arxiv.org\/abs\/1405.4763<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Eigenvalues of random matrices provide a prominent example of strongly correlated random variables.&nbsp;The issue of fluctuations of linear statistics on random matrices (sum functions of the eigenvalues)&nbsp;has a long history in the physics and mathematics literature.After a pedagogical introduction, I will present a recent universal covariance formula for large dimensional random matrices.&nbsp;I will provide some [&hellip;]<\/p>\n","protected":false},"author":20,"featured_media":0,"template":"","class_list":["post-996","seminar","type-seminar","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar\/996","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar"}],"about":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/types\/seminar"}],"author":[{"embeddable":true,"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/users\/20"}],"wp:attachment":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/media?parent=996"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}