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作者：Feng, J
作者单位：University of Massachusetts System; University of Massachusetts Amherst
摘要：Large deviation for Markov processes can be studied by Hamilton-Jacobi equation techniques. The method of proof involves three steps: First, we apply a nonlinear transform to generators of the Markov processes, and verify that limit of the transformed generators exists. Such limit induces a Hamilton-Jacobi equation. Second, we show that a strong form of uniqueness (the comparison principle) holds for the limit equation. Finally, we verify an exponential compact containment estimate. The large ...
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作者：Comets, Francis; Yoshida, Nobuo
作者单位：Universite Paris Cite; Kyoto University
摘要：In this paper we consider directed polymers in random environment with discrete space and time. For transverse dimension at least equal to 3, we prove that diffusivity holds for the path in the full weak disorder region, that is, where the partition function differs from its annealed value only by a non-vanishing factor. Deep inside this region, we also show that the quenched averaged energy has fluctuations of order 1. In complete generality (arbitrary dimension and temperature), we prove mon...
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作者：Adams, Stefan; Bru, Jean-Bernard; Koenig, Wolfgang
作者单位：Max Planck Society; Dublin Institute for Advanced Studies; Johannes Gutenberg University of Mainz; Leipzig University
摘要：We introduce two probabilistic models for N interacting Brownian motions moving in a trap in R-d under mutually repellent forces. The two models are defined in terms of transformed path measures on finite time intervals under a trap Hamiltonian and two respective pair-interaction Hamiltonians. The first pair interaction exhibits a particle repellency, while the second one imposes a path repellency. We analyze both models in the limit of diverging time with fixed number N of Brownian motions. I...
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作者：Tanner, Steve
作者单位：Eastern Oregon University
摘要：Let u be a pluriharmonic function on the unit ball in C-n. I consider the relationship between the set of points L-u on the boundary of the ball at which u converges nontangentially and the set of points L-u at which u converges along conditioned Brownian paths. For harmonic functions u of two variables, the result L-u (a.e.)= L-u has been known for some time, as has a counterexample to the same equality for three variable harmonic functions. I extend the L-u (a.e.)= result to pluriharmonic fu...
