4 сентября в 18:00 состоится заседание семинара кафедры Высшей математики и математической физики, ПОМИ, ауд. 203.
Докладчик: Frederic Klopp (Sorbonne Universite, Institut de Mathematiques de Jussieu — Paris Rive Gauche)
Тема: Localization revisited
We will present new estimates on the (normalized) eigenfunctions of a typical random Schrödinger operator in the localized regime. In the physics literature, in the localized regime, eigenfunctions are assumed to be uniformly decaying outside some ball of fixed radius at a rate dubbed the inverse localisation length. Up to now, mathematical results only show that eigenfunctions exhibit this decay behavior outside some large ball, the radius of the ball being dependent on its position. It is known that one cannot expect better for all eigenfunctions. But one may wonder how many eigenfunctions satisfy a better estimate or only this worse pоssible estimate. The talk is devoted to the answers to these questions. It is based on joint ongoing work with J. Schenker.