6 citations · 6 across the 5 of their papers we have counts for
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Random skeletons in high-dimensional lattice trees
Manuel Cabezas, Alexander Fribergh, Mark Holmes +1
We study the behaviour of the rescaled minimal subtree containing the origin and K random vertices selected from a random critical (sufficiently spread-out, and in dimensions d > 8…
Total disconnectedness and percolation for the supports of super-tree random measures
Edwin Perkins, Delphin Sénizergues
Super-tree random measures (STRMs) were introduced by Allouba, Durrett, Hawkes and Perkins as a simple stochastic model which emulates a superprocess at a fixed time. A STRM ar…
A stochastic differential equation for local times of super-Brownian motion
Jean-François Le Gall, Edwin Perkins
We show that local times of super-Brownian motion, or of Brownian motion indexed by the Brownian tree, satisfy an explicit stochastic differential equation. Our proofs rely on both…
Rescaling the spatial lambda Fleming-Viot process and convergence to super-Brownian motion
J. Theodore Cox, Edwin A. Perkins
We show that a space-time rescaling of the spatial Lamba-Fleming-Viot process of Barton and Etheridge converges to super-Brownian motion. This can be viewed as an extension of a re…
Renormalization of the two-dimensional Lotka--Volterra model
J. Theodore Cox, Edwin A. Perkins
We show that renormalized two-dimensional Lotka--Volterra models near criticality converge to a super-Brownian motion. This is used to establish long-term survival of a rare type f…