32 citations · 36 across the 3 of their papers we have counts for
4 papers
A lower bound for in range- bond percolation in two and three dimensions
Spencer Frei, Edwin Perkins
We use the connection between bond percolation and SIR epidemics to establish lower bounds for the critical percolation probability in and dimensions as the range becomes l…
On the boundary of the support of super-Brownian motion: with appendices
Carl Mueller, Leonid Mytnik, Edwin Perkins
We study the density X(t,x) of one-dimensional super-Brownian motion and find the asymptotic behaviour of P(0<X(t,x)<a) as a approaches 0, as well as the Hausdorff dimension of the…
Nonuniqueness for a parabolic SPDE with -Hölder diffusion coefficients
Carl Mueller, Leonid Mytnik, Edwin Perkins
Motivated by Girsanov's nonuniqueness examples for SDEs, we prove nonuniqueness for the parabolic stochastic partial differential equation (SPDE) \[\frac{\partial u}{\partial t}=\f…
Non-uniqueness for non-negative solutions of parabolic stochastic partial differential equations
K. Burdzy, C. Mueller, E. A. Perkins
Pathwise non-uniqueness is established for non-negative solutions of the parabolic stochastic pde where $\dot…