6 citations · 8 across the 8 of their papers we have counts for
10 papers
Wright-Fisher stochastic heat equations with irregular drifts
Clayton Barnes, Leonid Mytnik, Zhenyao Sun
Consider the -valued continuous random field solution to the one-dimensional stochastic heat equation \[ \partial_t u_t = \frac{1}{2}Δu_…
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…
Hausdorff Dimension of the Brownian Earthworm (WXML Winter 2017 Report)
Clayton Barnes, Krzysztof Burdzy, Alex Forney +3
Simulations support the conjecture that the dimension of the trace of Brownian earthworm is strictly greater than 3/2.
Effect of small noise on the speed of reaction-diffusion equations with non-Lipschitz drift
Clayton Barnes, Leonid Mytnik, Zhenyao Sun
We consider the -valued solution to the one dimensional stochastic reaction diffusion equation with Wright-Fisher noise \[\partial_t u= \…
Propagation of Chaos for reflecting diffusions with local-time dependent noise
Clayton Barnes
We prove existence and uniqueness of a reaction-diffusion equation whose diffusivity is a non-linear functional of the boundary temperature. We do this by studying systems of one-d…
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…
Hydrodynamic limit and Propagation of Chaos for Brownian Particles reflecting from a Newtonian barrier
Clayton Barnes
In 2001, Knight constructed a stochastic process modeling the one dimensional interaction of two particles, one being Newtonian in the sense that it obeys Newton's laws of motion,…
A Note on Jump Atlas Models
Clayton Barnes, Andrey Sarantsev
The market weight of a stock is its capitalization (cap) divided by the total market cap. Rank these weights from top to bottom. The capital distribution curve is a plot of weights…
The Lonely Runner Conjecture
Clayton Barnes
A detailed survey of the Lonely Runner Conjecture and its connection between Diophantine approximation and View-obstruction problems.