Paolo Dai Pra (Università degli Studi di Padova), Pierre-Yves Louis (Université de Poitiers)
(Pierre-Yves Louis)
Urn models have found several applications, from adaptive
design in medical treatments to random networks. In the first part of
the talk we review some of the most popular urn models, in particular
Polya's and Friedman's urns, and introduce the problem of interaction
and synchronization.
(Paolo Dai Pra)
In the second part we show how these models may be
reformulated in terms of reinforced random walks. The latter were introduced in the eighties to model situations where a random walker has a tendency to revisit familiar territory.
This approach allows to obtain sharp results concerning the long-time behavior of these dynamics.
