@prefix vivo: . @prefix edm: . @prefix dcterms: . @prefix dc: . @prefix skos: . @prefix ns0: . vivo:departmentOrSchool "Non UBC"@en ; edm:dataProvider "DSpace"@en ; dcterms:creator "Kemp, Todd"@en ; dcterms:issued "2017-05-15T21:57:37Z"@*, "2016-12-05T16:28"@en ; dcterms:description """Moving beyond the Wigner matrix paradigm, there is a vast literature on "band matrices" -- random matrices with entries that are not identically distributed.  In almost all cases, however, it is still assumed that the entries are independent (modulo the Hermitian condition), in order to prove convergence of the empirical eigenvalue distribution. One case where independence has been relaxed is block matrices.  If $X_n$ is a random Hermitian matrix with blocks of size $m\\times m$ that are independent, then operator valued free probability may be used to analyze the limit empirical spectral distribution (as discovered by Shlyakhtenko, and continued in the work of Bryc, Oraby, Rashidi Far and Speicher).  This analysis, so far, can only handle the case that $m$ is constant, or, dually, $m$ is proportional to $n$. In this talk, I will discuss recent joint work with my former student David Zimmermann, where we handle a much more general intermediate case.  We show that, if the matrix $X_n$ can be partitioned into independent ``blocks'' (not necessarily rectangular) each of size $o(\\log n)$, then the empirical spectral distribution converges to its mean in probability.  (The limit is usually not semicircular.)  The main tool we use is a mollified logarithmic Sobolev inequality, which I will discuss."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/61622?expand=metadata"@en ; dcterms:extent "31 minutes"@en ; dc:format "video/mp4"@en ; skos:note ""@en, "Author affiliation: University of California, San Diego"@en ; edm:isShownAt "10.14288/1.0347453"@en ; dcterms:language "eng"@en ; ns0:peerReviewStatus "Unreviewed"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "Banff International Research Station for Mathematical Innovation and Discovery"@en ; dcterms:rights "Attribution-NonCommercial-NoDerivatives 4.0 International"@en ; ns0:rightsURI "http://creativecommons.org/licenses/by-nc-nd/4.0/"@en ; ns0:scholarLevel "Faculty"@en ; dcterms:isPartOf "BIRS Workshop Lecture Videos (Banff, Alta)"@en ; dcterms:subject "Mathematics"@en, "Functional analysis"@en, "Probability theory and stochastic processes"@en, "Operator theory/algebras"@en ; dcterms:title "Random Matrices with Log-Range Correlations"@en ; dcterms:type "Moving Image"@en ; ns0:identifierURI "http://hdl.handle.net/2429/61622"@en .