A random polymer approach to the weak disorder phase of the Vertex Reinforced Jump Process

Vortrag von Prof. Dr. Christophe Sabot

Datum: 26.11.25  Zeit: 17.15 - 18.45  Raum: ETH HG G 43

The Vertex Reinforced Jump Process (VRJP) is a continuous-time process closely related to the linearly edge reinforced random walk. The recurrence/transience of the VRJP can be caracterized by the asymptotic behavior of a positive martingale : the VRJP is recurrent when the limit is null and transient when it is positive. Besides, the L^p integrability of that martingale is related to the diffusive behavior of the VRJP. 

A large part of the talk will be devoted to recall some key properties of the VRJP and to explain how that martingale appears and how it can be interpreted as the partition function of a non-directed polymer in a very specific 1-dependent potential. At the end, we will show new results about the L^p integrability of the martingale, using the polymer interpretation and taking inspiration from some works of Junk on directed polymers,

Based on a joint work with Q. Berger, A. Legrand and R. Poudevigne-Auboiron.