Date: Wednesday, March 27, 2013
Location: 4096 East Hall (4:10 PM to 5:00 PM)
Title: Large deviations for diffusions interacting through their ranks
Abstract: Systems of diffusion processes (particles) with rank-based interactions have been studied heavily due to their importance in stochastic portfolio theory and the intriguing relations with particle systems appearing in statistical physics. We will study the behavior of this particle system as the number of particles gets large. By obtaining a large deviations principle, we will show that the limiting dynamics can be described by a porous medium equation with convection, whereas paths of finite rate are given by solutions of appropriately tilted versions of this equation. This is the first instance of a large deviations principle for diffusions interacting both through the drift and the diffusion coefficients with the diffusion coefficients not being globally Lipschitz (and not even continuous). Based on joint work with A. Dembo, S.R.S. Varadhan and O. Zeitouni.
Speaker: Mykhaylo Shkolnikov
Institution: Berkeley
Event Organizer:
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