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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