4 papers
On the coming down from infinity of coalescing Brownian motions
Clayton Barnes, Leonid Mytnik, Zhenyao Sun
Consider a system of Brownian particles on the real line where each pair of particles coalesces at a certain rate according to their intersection local time. Assume that there are…
Billiards with Markovian reflection laws
Clayton Barnes, Krzysztof Burdzy, Carl-Erik Gauthier
We construct a class of reflection laws for billiard processes in the unit interval whose stationary distribution for the billiard position and its velocity is the product of the u…
Convergence of jump processes with stochastic intensity to Brownian motion with inert drift
Clayton Barnes
Consider a random walker on the nonnegative lattice, moving in continuous time, whose positive transition intensity is proportional to the time the walker spends at the origin. In…
The Lonely Runner Conjecture
Clayton Barnes
A detailed survey of the Lonely Runner Conjecture and its connection between Diophantine approximation and View-obstruction problems.