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DTSTAMP:20260424T143149Z
UID:668e4d9e6b2ed870400321@ist.ac.at
DTSTART:20241112T163000
DTEND:20241112T173000
DESCRIPTION:Speaker: Oleksii Kolupaiev\nhosted by Laszlo Erdös\nAbstract: 
 Let $W$ be an $N\\times N$ Wigner matrix and $D$ a self-adjoint deformatio
 n of the same size. It is known that for large $N$\, the resolvent $G(z)=(
 W+D-z)^{-1}$ of the deformed Wigner matrix $W+D$ concentrates around its d
 eterministic approximation already for $z$ just slightly above the real li
 ne. This concentration phenomenon also extends to the products of multiple
  resolvents\, such as $G(z_1)BG(z_2)$ for a deterministic matrix $B$. Such
  results are called the multi-resolvent local laws. In our work we extend 
 this framework by proving the 2-resolvent local law for $G_1(z_1)BG_2(z_2)
 $\, where $G_1$ and $G_2$ are resolvents of two differently deformed Wigne
 r matrices $W+D_1$ and $W+D_2$. In the talk we will discuss two applicatio
 ns of this result. The first one addresses the sensitivity of a quantum ev
 olution to perturbations via studying the so-called Loschmidt echo\, while
  the second one studies the decorrelation of eigenvectors of $W+D_1$ and $
 W+D_2$. The talk is based on a joint work with G. Cipolloni\, L. Erd{\\H o
 }s and J. Henheik.
LOCATION:Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101
 )\, ISTA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Oleksii Kolupaiev: Multi-resolvent local laws for differently defor
 med Wigner matrices and applications in mathematical physics
URL:https://talks-calendar.ista.ac.at/events/5380
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