### Andrey Sarantsev (University of Washington)

Title: Infinite Systems of Competing Brownian Particles

Abstract: Consider a system of infinitely many Brownian particles on the real line, which can be ordered starting from the bottom one. The bottom particle moves as a Brownian motion with drift one and diffusion one. All other particles move as standard Brownian motions. We are interested in the gaps between adjacent particles. The result of Pal and Pitman (2008) states that there is a copy of this system such that the gap process has stationary distribution equal to the infinite product of exponential distributions with rate two. We find a whole family of product-form stationary distributions for the gap process.