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作者：Miller, Jason; Sheffield, Scott
作者单位：Microsoft; Massachusetts Institute of Technology (MIT); University of Cambridge
摘要：We establish existence and uniqueness for Gaussian free field flow lines started at interior points of a planar domain. We interpret these as rays of a random geometry with imaginary curvature and describe the way distinct rays intersect each other and the boundary. Previous works in this series treat rays started at boundary points and use Gaussian free field machinery to determine which chordal processes are time-reversible when . Here we extend these results to whole-plane and establish con...
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作者：Ganguly, Shirshendu; Levine, Lionel; Peres, Yuval; Propp, James
作者单位：University of Washington; University of Washington Seattle; Cornell University; Microsoft; University of Massachusetts System; University of Massachusetts Lowell
摘要：We introduce a graph-theoretic model of interface dynamics called competitive erosion. Each vertex of the graph is occupied by a particle that can be either red or blue. New red and blue particles alternately get emitted from their respective bases and perform random walk. On encountering a particle of the opposite color they kill it and occupy its position. We prove that on the cylinder graph (the product of a path and a cycle) an interface spontaneously forms between red and blue and is main...
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作者：Kosygina, Elena; Zerner, Martin P. W.
作者单位：City University of New York (CUNY) System; Baruch College (CUNY); Eberhard Karls University of Tubingen
摘要：We provide sufficient conditions for the validity of a dichotomy, i.e. zero-one law, between recurrence and transience of general frog models. In particular, the results cover frog models with i.i.d. numbers of frogs per site where the frog dynamics are given by quasi-transitive Markov chains or by random walks in a common random environment including super-critical percolation clusters on . We also give a sufficient and almost sharp condition for recurrence of uniformly elliptic frog processe...
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作者：Jagannath, Aukosh; Tobasco, Ian
摘要：In this paper we study the Parisi variational problem for mixed p-spin glasses with Ising spins. Our starting point is a characterization of Parisi measures whose origin lies in the first order optimality conditions for the Parisi functional, which is known to be strictly convex. Using this characterization, we study the phase diagram in the temperature-external field plane. We begin by deriving self-consistency conditions for Parisi measures that generalize those of de Almeida and Thouless to...
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作者：Basak, Anirban; Mukherjee, Sumit
作者单位：Duke University; Columbia University
摘要：We consider the Potts model with q colors on a sequence of weighted graphs with adjacency matrices , allowing for both positive and negative weights. Under a mild regularity condition on we show that the mean-field prediction for the log partition function is asymptotically correct, whenever . In particular, our results are applicable for the Ising and the Potts models on any sequence of graphs with average degree going to . Using this, we establish the universality of the limiting log partiti...
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作者：Gueneysu, B.; Matte, O.; Moller, J. S.
作者单位：Humboldt University of Berlin; Aarhus University
摘要：We discuss Hilbert space-valued stochastic differential equations associated with the heat semi-groups of the standard model of non-relativistic quantum electrodynamics and of corresponding fiber Hamiltonians for translation invariant systems. In particular, we prove the existence of a stochastic flow satisfying the strong Markov property and the Feller property. To this end we employ an explicit solution ansatz. In the matrix-valued case, i.e., if the electron spin is taken into account, it i...
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作者：Cerny, Jiri; Wassmer, Tobias
作者单位：University of Vienna
摘要：We study the Metropolis dynamics of the simplest mean-field spin glass model, the random energy model. We show that this dynamics exhibits aging by showing that the properly rescaled time change process between the Metropolis dynamics and a suitably chosen 'fast' Markov chain converges in distribution to a stable subordinator. The rescaling might depend on the realization of the environment, but we show that its exponential growth rate is deterministic.
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作者：Hofmanova, Martina; Roeger, Matthias; von Renesse, Max
作者单位：Max Planck Society; Technical University of Berlin; Dortmund University of Technology; Leipzig University
摘要：We study a stochastically perturbed mean curvature flow for graphs in over the two-dimensional unit-cube subject to periodic boundary conditions. The stochastic perturbation is a one dimensional white noise acting uniformly in all points of the surface in normal direction. We establish the existence of a weak martingale solution. The proof is based on energy methods and therefore presents an alternative to the stochastic viscosity solution approach. To overcome difficulties induced by the dege...
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作者：Neuman, Eyal; Zheng, Xinghua
作者单位：University of Rochester; Hong Kong University of Science & Technology
摘要：We study the maximal displacement of a one dimensional subcritical branching random walk initiated by a single particle at the origin. For each let be the rightmost position reached by the branching random walk up to generation n. Under the assumption that the offspring distribution has a finite third moment and the jump distribution has mean zero and a finite probability generating function, we show that there exists such that the function
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作者：Gu, Yu
作者单位：Stanford University
摘要：In this paper, we study high order correctors in stochastic homogenization. We consider elliptic equations in divergence form on , with the random coefficients constructed from i.i.d. random variables. We prove moment bounds on the high order correctors and their gradients under dimensional constraints. It implies the existence of stationary correctors and stationary gradients in high dimensions. As an application, we prove a two-scale expansion of the solutions to the random PDE, which identi...
