2021/12/22 by Floreani, Simone, Jansen, Sabine, Redig, Frank +1
#60J70 #60K35 #82C22 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Probability (math.PR)
paper · doi:10.48550/arxiv.2112.11885
In this paper we derive intertwining relations for a broad class of conservative particle systems both in discrete and continuous setting. Using the language of point process theory, we are able to derive a natural framework in which duality and intertwining can be formulated. We prove falling factorial and orthogonal polynomial intertwining relations in a general setting. These intertwinings unite the previously found classical and orthogonal self-dualities in the context of discrete particle systems and provide new dualities for several interacting systems in the continuum. We also introduce a new process, the symmetric inclusion process in the continuum, for which our general method applies and yields generalized Meixner polynomials as orthogonal self-intertwiners.