Abstract:

The Partially Asymmetric Self Exclusion Processes (PASEP) is a physical model representing the displacement of particles on a path with different parameters. It can be viewed as a Markov chain whose steady-state probabilities are closely related to the combinatorics of Catalan objects and of permutations. For instance, in 2007 Corteel and Williams proved that these probabilities can be described using objects called "permutation tableaux" themselves in bijection with permutations. More recently, Mandelshtam and Viennot gave an interpretation of the probabilities of the 2-PASEP, a generalization of the PASEP with two types of particles, using "Rhombic alternative tableaux" and "assemblée of permutations". In this talk I will present the different approach to describe these probabilities and an interpretation using a generalization of permutations called "partially signed permutations".