Abstract:
In this talk I will review some results obtained about two closely related models, the directed and non-directed linearly edge reinforced random walks. The directed edge reinforced random walk can be represented in terms of a (non-reversible) random walk in i.i.d. random environment, with Dirichlet distribution at each side. On the other side, the non-directed Edge reinforced random walk can be represented as a random walk in (higly-correlated) random conductances. Starting from very standard results as the de Finetti theorems and Polya urns, I will explain the quite different approaches which have been taken to understand these models, the remaining open questions, and some links they have with several other models or questions. At the end, I will give a glimpse at more recent works with Baccalado and Tarrès, that show that these two models belong to a larger common familly of processes.
Biography:
Christophe Sabot is Professor at University Claude Bernard Lyon 1 and senior member of the Institut universitaire de France since 2022. His main research areas concern random walks, random environment, and self-interacting processes.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.