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6 papers · 2 filters
Time-reversal and elliptic boundary value problems
Zhen-Qing Chen, Tusheng Zhang
In this paper, we prove that there exists a unique, bounded continuous weak solution to the Dirichlet boundary value problem for a general class of second-order elliptic operators…
Global Heat Kernel Estimates for Fractional Laplacians in Unbounded Open Sets
Zhen-Qing Chen, Joshua Tokle
In this paper, we derive global sharp heat kernel estimates for symmetric alpha-stable processes (or equivalently, for the fractional Laplacian with zero exterior condition) in two…
Non-extinction of a Fleming-Viot particle model
Mariusz Bieniek, Krzysztof Burdzy, Sam Finch
We consider a branching particle model in which particles move inside a Euclidean domain according to the following rules. The particles move as independent Brownian motions until…
Regularity of harmonic functions for a class of singular stable-like processes
Richard F. Bass, Zhen-Qing Chen
We consider the system of stochastic differential equations dX_t=A(X_{t-}) dZ_t, where Z_t^1, ..., Z^d_t are independent one-dimensional symmetric stable processes of order α, and…
A combinatorial analysis of interacting diffusions
Sourav Chatterjee, Soumik Pal
We consider a particular class of n-dimensional homogeneous diffusions all of which have an identity diffusion matrix and a drift function that is piecewise constant and scale inva…
On the diameter of the set of satisfying assignments in random satisfiable k-CNF formulas
Uriel Feige, Abraham D. Flaxman, Dan Vilenchik
It is known that random k-CNF formulas have a so-called satisfiability threshold at a density (namely, clause-variable ratio) of roughly 2^k\ln 2: at densities slightly below this…