SPMES: The asymptotic distribution of the condition number for random ci... - Gerardo Barrera Vargas

Seminário de Probabilidade e Mecânica Estatística
Título: The asymptotic distribution of the condition number for random circulant matricess
Palestrante: Gerardo Barrera Vargas, IST Lisboa
Playlist dos videos: bit.ly/30ZkHWe
Resumo: In this presentation we study the limiting distribution for the joint-law of the largest and the smallest singular values for random circulant matrices with generating sequence given by independent and identically distributed random elements satisfying the so-called Lyapunov condition. Under an appropriated normalization, the joint-law of the extremal singular values converges in distribution, as the matrix dimension tends to infinity, to an independent product of Rayleigh and Gumbel laws. The latter implies that a normalized condition number converges in distribution to a Fréchet law as the dimension of the matrix increases. Roughly speaking, the condition number measures how much the output value of a linear system can change by a small perturbation in the input argument. The proof relies on the celebrated Einmahl--Komlós--Major--Tusnády coupling. This is based in a paper with Paulo Manrique, Extremes 2022.
Apoio:
IMPA
Instituto Superior Técnico de Lisboa
UFBA
UFMG
UFRGS
UFRJ
Unicamp
Universidade do Porto
USP
Comitê científico:
Luiz Renato Fontes (USP)
Tertuliano Franco (UFBA)
Nancy Lopes Garcia (Unicamp)
Patrícia Gonçalves (IST, Lisboa)
Marcelo Hilário (UFMG)
Roberto Imbuzeiro (Coordenador, IMPA)
Claudio Landim (Coordenador, IMPA)
Adriana Neumann (UFRGS)
Serguei Popov (UP, Porto)
Glauco Valle (UFRJ)
Redes Sociais do IMPA: linktr.ee/impabr
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