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mega:seminaire [2026/10/02 18:38] – Raphaël BUTEZmega:seminaire [2026/10/02 18:38] (Version actuelle) – Raphaël BUTEZ
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     * 15h00-16h00:  Séminaire de **[[https://ekvv.uni-bielefeld.de/pers_publ/publ/PersonDetail.jsp?personId=148940020&lang=EN|Noah Aygün]]** //Products of characteristic polynomials in complex symmetric, self-dual, and Ginibre elliptic ensembles.// \\     * 15h00-16h00:  Séminaire de **[[https://ekvv.uni-bielefeld.de/pers_publ/publ/PersonDetail.jsp?personId=148940020&lang=EN|Noah Aygün]]** //Products of characteristic polynomials in complex symmetric, self-dual, and Ginibre elliptic ensembles.// \\
-Abstract: It has been conjectured that generic spectral statistic in the bulk and at the edge in all 38 symmetry classes of non-Hermitian random matrix theory follows a threefold way. The simplest symmetry classes that display these limiting universality classes are Gaussian complex symmetric, complex self-dual and complex Ginibre random matrices. In the Cartan classification these are labelled as class A, AI$^\dag$ and AII$^\dag$, respectively. +Abstract: It has been conjectured that generic spectral statistic in the bulk and at the edge in all 38 symmetry classes of non-Hermitian random matrix theory follows a threefold way. The simplest symmetry classes that display these limiting universality classes are Gaussian complex symmetric, complex self-dual and complex Ginibre random matrices. In the Cartan classification these are labelled as class A, AI$^\dagger$ and AII$^\dagger$, respectively. 
 Despite recent progress it remains difficult to obtain general multi-point density correlation functions in the latter two classes. Here, we will consider expectation values of products of pairs of complex conjugated characteristic polynomials as observables in these three ensembles, including their elliptic deformation.  Explicit results will be presented for finite matrix size $N$ and in the large-$N$ limit.  Despite recent progress it remains difficult to obtain general multi-point density correlation functions in the latter two classes. Here, we will consider expectation values of products of pairs of complex conjugated characteristic polynomials as observables in these three ensembles, including their elliptic deformation.  Explicit results will be presented for finite matrix size $N$ and in the large-$N$ limit. 
  
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  • Dernière modification : 2026/10/02 18:38
  • de Raphaël BUTEZ