Mark Rychnovsky, Columbia University

Abstract: Sticky Brownian motions behave as independent Brownian motions when they are separated and interact when they touch, so that the coincidence time has positive Lebesgue measure with positive probability. For a specific sticky interaction we show that as the number of particles, and the time the particles are allowed to evolve are simultaneously sent to infinity, the fluctuations of the extremal particle are given by the GUE Tracy-Widom distribution. The proof involves realizing a specific sticky interaction as the limit of an exactly solvable statistical mechanics model, the Beta random walk in random environment, and using this to derive exact integral formulas.

This is joint work with Guillaume Barraquand.