The National Seminar on Probability and Statistics will be held on May 31, 2017 (Wednesday), at 2 p.m. in Room 403 of IMI - BAS.

Jozsef  Lorinczi will deliver a lecture on:

Some spectral properties of non-local Schrödinger operators and related jump processes

Abstract: A non-local Schrödinger operator is the sum of a pseudo-differential operator (such as the Laplacian with fractional exponents) and a multiplication operator called potential. Dependent on the behaviour of the potential at infinity, the spectrum of the operator sum may differ strongly from the spectrum of the unperturbed pseudo-differential operator, and a whole range of spectral and semigroup properties emerge. The spectral problem can be analysed by turning it into a problem of probability via a Feynman-Kac representation, and looking at a random process evolving in a potential landscape. In this talk I will explain this relationship, and survey recent results on the properties of ground states.