Sabine Jansen
Biography
Sabine Jansen, LMU Munich, statistical mechanics and probability theory, in particular cluster expansions, Markov processes, point processes.
Title: Duality, interacting particle systems, and infinite-dimensional orthogonal polynomials
Abstract: Studying the time-evolution of a many-particle system is a difficult task. For some interacting particle systems in Z^d, duality and intertwining allow to map the time evolution of one- or two-point correlation functions of a many-particle system to the time evolution of a one- or two-particle system, a considerable simplification. Often duality functions are products of univariate orthogonal polynomials, one for each site of the lattice. In the talk I will explain how to generalize these dualities, and the algebraic approach with representations of Lie algebras, to particles in R^d. This brings in Lévy point processes and infinite-dimensional orthogonal polynomials.
Based on joint work with Simone Floreani, Frank Redig and Stefan Wagner.
