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SUMMARY:Ofer Zeitouni (Weizmann Institute of Science)
DTSTART:20200420T113000Z
DTEND:20200420T123000Z
DTSTAMP:20260423T024024Z
UID:HSPETDS/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HSPETDS/1/">
 Stability and instability of spectrum for noisy perturbations of non-Hermi
 tian matrices</a>\nby Ofer Zeitouni (Weizmann Institute of Science) as par
 t of Horowitz seminar on probability\, ergodic theory and dynamical system
 s\n\nLecture held in 309.\n\nAbstract\nWe discuss the spectrum of high dim
 ensional non-Hermitian matrices under small noisy perturbations. That spec
 trum can be extremely unstable\, as the maximal nilpotent matrix JN with J
 N(i\,j)=1 iff j=i+1 demonstrates. Numerical analysts studied worst case pe
 rturbations\, using the notion of pseudo-spectrum. Our focus is on finding
  the locus of most eigenvalues (limits of density of states)\, as well as 
 studying stray eigenvalues ("outliers"). I will describe the background\, 
 show some fun and intriguing simulations\, and present some theorems and w
 ork in progress concerning eigenvectors. No background will be assumed. Th
 e talk is based on joint work with Anirban Basak\, Elliot Paquette\, and M
 artin Vogel.\n
LOCATION:https://researchseminars.org/talk/HSPETDS/1/
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