Abstract:We will discuss various models of self-interacting random walks, in particular the Vertex-Reinforced Random Walk (VRRW) and some non-reversible generalizations of the Edge-Reinforced Random Walk (*-ERRW) motivated by Bayesian statistics for variable order Markov Chains. Contrary to the VRRW, the *-ERRW  is partially exchangeable in the sense of Diaconis and Freedman (1982), and its mixing measure can be explicitly computed. 

Both the VRRW and the *-ERRW can be associated to a continuous process, respectively called the continuous vertex-reinforced random walk (cVRRW) and the *-Vertex Reinforced Random Walk (*-VRJP), both of which are in general not partially exchangeable. The *-VRJP however satisfies several fascinating properties, and in particular a random Schrödinger representation, which will be very useful in the study of recurrence/transience properties.

Based on joint works with S. Bacallado and C. Sabot, and with Shuo Qin.

Bio: Pierre Tarrès is a Professor of Mathematics at NYU Shanghai, and an Associated Professor at the Courant Institute of Mathematical Sciences in New York. He was a Research Director at the National Center for Scientific Research (CNRS) in Paris from 2014 to 2016, and an Associate Professor at the University of Oxford from 2005 to 2014.

Prof. Tarrès is an expert on self-interacting random processes, particularly reinforced random walks, and their relationship with stochastic algorithms and learning processes in game theory. He was awarded a Leverhulme Prize in 2006, the Prix des Annales de l'Institut Henri Poincaré in 2008. He has been an Associate Editor at the Annals of Applied Probability since 2019.