531 citations
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22 papers · 1 filter
Pathwise uniqueness for stochastic heat equations with Hölder continuous coefficients: the white noise case
Leonid Mytnik, Edwin Perkins
We prove pathwise uniqueness for solutions of parabolic stochastic pde's with multiplicative white noise if the coefficient is Hölder continuous of index . The method of pro…
Local Bootstrap Percolation
Janko Gravner, Alexander E. Holroyd
We study a variant of bootstrap percolation in which growth is restricted to a single active cluster. Initially there is a single active site at the origin, while other sites of Z^…
On the Cluster Size Distribution for Percolation on Some General Graphs
Antar Bandyopadhyay, Jeffrey Steif, Adam Timar
We show that for any Cayley graph, the probability (at any ) that the cluster of the origin has size n decays at a well-defined exponential rate (possibly 0). For general graphs…
Degenerate Stochastic Differential Equations for Catalytic Branching Networks
Sandra M. Kliem
Uniqueness of the martingale problem corresponding to a degenerate SDE which models catalytic branching networks is proven. This work is an extension of a paper by Dawson and Perki…
Degenerate stochastic differential equations arising from catalytic branching networks
Richard F. Bass, Edwin A. Perkins
We establish existence and uniqueness for the martingale problem associated with a system of degenerate SDE's representing a catalytic branching network. For example, in the hyperc…
A random walk on Z with drift driven by its occupation time at zero
Iddo Ben-Ari, Mathieu Merle, Alexander Roitershtein
We consider a nearest neighbor random walk on the one-dimensional integer lattice with drift towards the origin determined by an asymptotically vanishing function of the number of…