Duality, intertwining and orthogonal polynomials for continuum interacting particle systems
Duality is a powerful tool for studying interacting particle systems, i.e., continuous-time Markov processes describing many particles say on the lattice Zd. In recent years interesting dualities have been proven that involve falling factorials and orthogonal polynomials; the orthogonality measure is the reversible measure of the Markov process. I'll address generalizations to particles moving in the continuum rather than on the lattice. Examples include independent diffusions and free Kawasaki, which have been investigated before, and a continuum version of the symmetric inclusion process, which is new. The falling factorials turn out to be related to Lenard's K-transform. The relevant notion of orthogonal polynomials belongs to infinite-dimensional analysis, chaos decompositions and multiple stochastic integrals. The talk is based on joint work with Simone Floreani and Frank Redig (TU Delft) and Stefan Wagner (LMU Munich).