**Date & Time:** Thursday, August 07, 2014, 16:00-17:00.

**Venue:** Ramanujan Hall

**Title:** Synchronization Via Interacting Reinforcement

**Speaker:** Neeraja Sahasrabudhe, IIT Bombay

**Abstract:** We consider a system of urns of Friedmantype, with balls of two colours,
such that the reinforcement of each urn depends on both the content of that urn and the
average content of all the urns. We study the fraction of balls of each colour in each urn
Z_t(i) and the average fraction Z_t and obtain the rates of convergence of Var(Z_t(i))
and Var(Z_t). We will also discuss the work of Dai Pra, Minelli and PierreYves Louis
on interacting Polya urns.

In this case, it is shown that the urns synchronize almost surely and a normal approximation for a large number of urns is obtained. By synchronization we mean that the fraction of balls of a given colour converges almost surely to the same limit for all urns.