Point processes and random resonancesOberseminar Stochastics

by Illia Karabash (University of Bonn)

Thursday 21 Nov 2024, 16:30 → 17:30 Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

Resonances of wave equations describe localization of energy on non-
homogeneities for large times. The asymptotics of resonances is usually stud-
ied on different levels of detalization by means of counting functions in growing
complex sets and by resonance- free regions. In the case of stochastic me-
dia, it is desirable to describe random sets of resonances by point processes.
The aim of the talk is to combine asymptotic studies of resonances with the
stochastic settings where a 3-D Schrödinger operator has a singular random
potential consisting of a finite number of delta-potentials with random posi-
tions. If time allows us, more sophisticated stochastic models stemming from
Photonics will be also discussed. The talk is based partially on the joint paper
with Sergio Albeverio (https://doi.org/10.1007/978-3-030-68490-7_2).