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5 papers · 2 filters
Continuity of the SLE trace in simply connected domains
Christophe Garban, Steffen Rohde, Oded Schramm
We prove that the trace in any simply connected domain is continuous (except possibly near its endpoints) if . We also prove an SLE analog of Makarov's Theorem abo…
On notions of harmonicity
Zhen-Qing Chen
In this paper, we address the equivalence of the analytic and probabilistic notions of harmonicity in the context of general symmetric Hunt processes on locally compact separable m…
Eigenvectors of random graphs: Nodal domains
Yael Dekel, James R. Lee, Nathan Linial
We initiate a systematic study of eigenvectors of random graphs. Whereas much is known about eigenvalues of graphs and how they reflect properties of the underlying graph, relative…
Differentiability of stochastic flow of reflected Brownian motions
Krzysztof Burdzy
We prove that a stochastic flow of reflected Brownian motions in a smooth multidimensional domain is differentiable with respect to its initial position. The derivative is a linear…
Stationary distributions for diffusions with inert drift
Richard F. Bass, Krzysztof Burdzy, Zhen-Qing Chen +1
Consider a reflecting diffusion in a domain in that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary…