Probability Seminar: Kilian Raschel

  • Date: 10/21/2015
  • Time: 15:00
Kilian Raschel, Pacific Institute for the Mathematical Sciences and Université de Tours

University of British Columbia


Discrete harmonic functions in the quadrant


In this talk we shall be interested in discrete harmonic functions in cones (in particular, in the quarter plane). The generating function of these harmonic functions satisfies a functional equation (closed to a well-known functional equation that appears in the context of enumeration of confined walks in combinatorics). We shall show the link between these harmonic functions and a one-parameter family of conformal mappings. One of the motivations to that study is to condition (in the sense of Doob) random walks never to leave cones.

Other Information: 

Location: ESB 2012