Constructing processes with duality properties
vendredi 16 janvier 2015, 11h00 - 12h00
Duality and self-duality are very useful properties of Markov processes, that allow to connect two at first sight unrelated processes via a duality function.
This very often leads to important simplifications such as « from continuous to discrete processes, from many to a few particles, from asymmetric processes to symmetric processes ».
We illustrate this method in the context of a new class of interacting particle systems with attractive interaction, and associated models of heat conduction and energy redistribution such as the famous KMP model. We show how these processes can be obtained constructively from some basic objects (Casimir operator, co-product) in the Lie algebra SU(1,1). We then show how using the corresponding deformed algebra leads naturally to their corresponding asymmetric analogues.