4 problems

Consider the infinite Brownian particle systems described by the order-statistics formulation, with particles whose asymmetry parameter satisfies $p\neq 1/2$, and their connections…

Uniqueness conjecture. The distribution $\pi_0$ is the unique stationary distribution of the gap sequence of the infinite Atlas model. The conjecture concerns the long-time behavio…

Fix $delta>0$. In the infinite Atlas model with Atlas drift $delta$, let $X_{(k)}(0)$, $k=1,2,ldots$, be initially ordered points of a Poisson process with rate $2delta$ on…

Let $B_{(0)}(t)$ denote the position at time $t$ of the particle initially at $0$ in the Harris system of ordered Brownian motions. A process is Markov if its future conditional la…