178 citations
- University of TorontoCA40 papers
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- Centre National de la Recherche ScientifiqueFR6 papers
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7 papers · 2 filters
Vertex-reinforced random walk on arbitrary graphs
Stanislov Volkov
Vertex-Reinforced Random Walk (VRRW), defined by Pemantle (1988a), is a random process in a continuously changing environment which is more likely to visit states it has visited be…
On a singular semilinear elliptic boundary value problem and the boundary Harnack principle
Siva Athreya
We consider the singular boundary-value problem Δu = f(u) in D; u|_dD= phi, where 1. D is a bounded C^2-domain of R^d, d >= 3 2. f: (0,1) -> (0,1) is a locally Hölder continuous fu…
Monotonicity property for a class of semilinear partial differential equations
Siva Athreya
We establish a monotonicity property in the space variable for the solutions of an initial boundary value problem concerned with the parabolic partial differential equation connect…
Lattice trees, percolation and super-Brownian motion
Gordon Slade
This paper surveys the results of recent collaborations with Eric Derbez and with Takashi Hara, which show that intergrated super-Brownian excursion (ISE) arises as the scaling lim…
Mean-field lattice trees
Christian Borgs, Jennifer Chayes, Remco van der Hofstad +1
We introduce a mean-field model of lattice trees based on embeddings into of abstract trees having a critical Poisson offspring distribution. This model provides a combinato…
Uniqueness for a class of one-dimensional stochastic PDEs using moment duality
Siva Athreya, Roger Tribe
For independent nearest-neighbour bond percolation on Z^d with d >> 6, we prove that the incipient infinite cluster's two-point function and three-point function converge to those…