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2016-09-07: Columbia Probability Seminar

"Competing Brownian Particle Systems"

By: "Ioannis Karatzas "

Date & Time:

Wednesday, September 7th, 2016, 5:00pm-6:00pm


Columbia University, Math 507


We consider systems of diffusing particles, whose local characteristics are assigned in terms of their ranks. We construct the associated multidimensional diffusions, and discuss questions of strength and pathwise uniqueness for the stochastic equations that realize them. Multi-dimensional and perturbed versions of the Tanaka equation arise, and are studied in some detail ? as are questions regarding triple (or higher-order) collisions, which play here an important role. When we allow for elastic collisions between particles, the ranked versions of the resulting diffusive motions arise as scaled limits of asymmetric, exclusion-type interacting particle systems. (Survey of joint works with E.R. Fernholz, T. Ichiba, S. Pal, V. Prokaj and M. Shkolnikov.)