Margherita Disertori

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Edge reinforced random walk (ERRW) and vertex reinforced jump processes
(VRJP) are history dependent stochastic processes, where the particle
tends to come back more often on sites it has already visited in the past.
For a particular scheme of reinforcement these processes are random walks
in a random environment whose mixing measure can be related to a nonlinear
sigma model introduced in the context of random matrix models for quantum
diffusion. This relation allows to prove, in particular, transience for
weak reinforcement of both processes, in d larger or equal to 3. I will
give a review of the problem and some recent results.

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Hausdorff Centre for Mathematics, Bonn
Seminar room, theory building
Contact: Martin Zirnbauer