Representations of the VRJP as a mixture of Markov processes and Martin boundary

par Thomas Gérard

jeudi 12 déc. 2019, 14:00 → 15:00 Europe/Paris

Fokko du Cloux (La Doua, Bâtiment Braconnier)

The Vertex Reinforced Jump Process on weighted graphs can be represented as a mixture of Markov processes, i.e. as a random walk in random environment. This representation can be constructed using a certain random Schrödinger operator. This talk concerns the classification of possible representations of the VRJP. We show that any such representation involves the same random Schrödinger operator, and a positive harmonic function for this operator. Using the notion of Martin boundary, we can then give a more general form for all representations. This relies on work by C. Sabot, P. Tarrès and X. Zeng.