| 概要 | Systems of many diffusion processes (particles) with rank-based
interactions appear in stochastic portfolio theory and in statistical
physics. In this talk (based on a joint work with Shkolnikov, Varadhan
and Zeitouni), we consider tail behavior (i.e. large deviations), for
such systems, out of which we find that the limiting dynamics follows
a porous medium equation with convection, and moreover, that paths of
finite exponential decay rate correspond to solutions of appropriately
tilted versions of this equation. This is the first instance of a
large deviations principle for diffusions interacting via diffusion
coefficients that are not globally Lipschitz (nor even continuous). |