Speaker: Leonardo Robol Affiliation: Università di Pisa Venue: Aula Magna, Dipartimento di Matematica Time: Thursday, 24/02/2022, 11:00
Title: Sampling the eigenvalues of random matrices
Random matrices (that is, matrices with random variables as entries) appear in several areas of mathematics and physics. Often, one is interested in sampling their eigenvalues (which are again random variables); we briefly recap the main tools that can be used to sample the joint eigenvalue distribution for Hermitian matrices from the Gaussian unitary Ensemble (GUE) with O(n^2) flops, and discuss how similar ideas can be used to efficiently perform the analogous operation for Haar-distributed orthogonal or unitary matrices.
The latter operation requires to find a suitable compact canonical form for upper Hessenberg unitary matrices obtained by reducing random orthogonal/unitary matrices, and then efficiently operate on this compact representation to compute the eigenvalues.
Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4
A reminder of tomorrow morning's seminar.
-------- Messaggio Inoltrato -------- Oggetto: Seminar announcement Data: Fri, 18 Feb 2022 20:14:33 +0100 Mittente: Fabio Durastante fabio.durastante@unipi.it A: numpi@lists.dm.unipi.it
Speaker: Leonardo Robol Affiliation: Università di Pisa Venue: Aula Magna, Dipartimento di Matematica Time: Thursday, 24/02/2022, 11:00
Title: Sampling the eigenvalues of random matrices
Random matrices (that is, matrices with random variables as entries) appear in several areas of mathematics and physics. Often, one is interested in sampling their eigenvalues (which are again random variables); we briefly recap the main tools that can be used to sample the joint eigenvalue distribution for Hermitian matrices from the Gaussian unitary Ensemble (GUE) with O(n^2) flops, and discuss how similar ideas can be used to efficiently perform the analogous operation for Haar-distributed orthogonal or unitary matrices.
The latter operation requires to find a suitable compact canonical form for upper Hessenberg unitary matrices obtained by reducing random orthogonal/unitary matrices, and then efficiently operate on this compact representation to compute the eigenvalues.
Meeting link: https://hausdorff.dm.unipi.it/b/leo-xik-xu4
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Fabio Durastante