Mathematics

Consider a finite system of competing Brownian particles on the real line. Each particle moves as a Brownian motion with drift and diffusion coefficients, depending on its rank. Consider the gaps between consecutive particles; under some conditions, it converges exponentially fast to a certain stationary distribution. The question is, how exactly fast? We find estimates of the exponent of convergence. Our main tool is Foster-Lyapunov functions theory; we also apply stochastic comparison techniques.