Sabine Jansen (LMU München)
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 S. Floreani, F. Redig and S.Wagner.
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