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作者：Sethuraman, Sunder; Varadhan, S. R. S.
作者单位：University of Arizona; New York University
摘要：Laws of large numbers, starting from certain nonequilibrium measures, have been shown for the integrated current across a bond, and a tagged particle in one-dimensional symmetric nearest-neighbor simple exclusion [Ann. Inst. Henri Poincare Probab. Stat. 42 (2006) 567-577]. In this article, we prove corresponding large deviation principles and evaluate the rate functions, showing different growth behaviors near and far from their zeroes which connect with results in [J. Stat. Phys. 136 (2009) 1...
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作者：Hammond, Alan
作者单位：University of Oxford
摘要：We consider a random walk on a supercritical Galton-Watson tree with leaves, where the transition probabilities of the walk are determined by biases that are randomly assigned to the edges of the tree. The biases are chosen independently on distinct edges, each one according to a given law that satisfies a logarithmic nonlattice condition. We determine the condition under which the walk is sub-ballistic, and, in the sub-ballistic regime, we find a formula for the exponent gamma epsilon (0, 1) ...
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作者：Aidekon, Elie
作者单位：Eindhoven University of Technology
摘要：We consider the minimum of a super-critical branching random walk. Addario-Berry and Reed [Ann. Probab. 37 (2009) 1041-1079] proved the tightness of the minimum centered around its mean value. We show that a convergence in law holds, giving the analog of a well-known result of Bramson [Mem. Amer Math. Soc. 44 (1983) iv+190] in the case of the branching Brownian motion.
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作者：Corwin, Ivan; Quastel, Jeremy
作者单位：New York University; University of Toronto
摘要：We consider the weakly asymmetric limit of simple exclusion process with drift to the left, starting from step Bernoulli initial data with rho(-) < rho(+) so that macroscopically one has a rarefaction fan. We study the fluctuations of the process observed along slopes in the fan, which are given by the Hopf-Cole solution of the Kardar-Parisi-Zhang (KPZ) equation, with appropriate initial data. For slopes strictly inside the fan, the initial data is a Dirac delta function and the one point dist...
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作者：Asselah, Amine; Gaudilliere, Alexandre
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：We consider internal diffusion limited aggregation in dimension larger than or equal to two. This is a random cluster growth model, where random walks start at the origin of the d-dimensional lattice, one at a time, and stop moving when reaching a site that is not occupied by previous walks. It is known that the asymptotic shape of the cluster is a sphere. When the dimension is two or more, we have shown in a previous paper that the inner (resp., outer) fluctuations of its radius is at most of...
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作者：Tugaut, Julian
作者单位：University of Bielefeld
摘要：We investigate the convergence of McKean-Vlasov diffusions in a non-convex landscape. These processes are linked to nonlinear partial differential equations. According to our previous results, there are at least three stationary measures under simple assumptions. Hence, the convergence problem is not classical like in the convex case. By using the method in Benedetto et al. [J. Statist. Phys. 91 (1998) 1261-1271] about the monotonicity of the free-energy, and combining this with a complete des...
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作者：Lawler, Gregory F.; Werness, Brent M.
作者单位：University of Chicago
摘要：In this paper we define and prove of the existence of the multi-point Green's function for SLE a normalized limit of the probability that an SLE kappa curve passes near to a pair of marked points in the interior of a domain. When kappa <8 this probability is nontrivial, and an expression can be written in terms two-sided radial SLE. One of the main components to our proof is a refinement of a bound first provided by Beffara [Ann. Probab. 36 (2008) 14211452]. This work contains a proof of this ...
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作者：Gloter, Arnaud; Martinez, Miguel
作者单位：Universite Paris Saclay; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In this paper, we consider two skew Brownian motions, driven by the same Brownian motion, with different starting points and different skewness coefficients. We show that we can describe the evolution of the distance between the two processes with a stochastic differential equation. This S.D.E. possesses a jump component driven by the excursion process of one of the two skew Brownian motions. Using this representation, we show that the local time of two skew Brownian motions at their first hit...
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作者：Lawler, Gregory F.; Zhou, Wang
作者单位：University of Chicago; National University of Singapore
摘要：Developing the theory of two-sided radial and chordal SLE, we prove that the natural parametrization on SLE kappa curves is well defined for all kappa <8. Our proof uses a two-interior-point local martingale.
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作者：Duminil-Copin, H.; Van Enter, A. C. D.
作者单位：University of Geneva; University of Groningen
摘要：Bootstrap percolation models have been extensively studied during the two past decades. In this article, we study the following anisotropic boot-strap percolation model: the neighborhood of a point (m, n) is the set {(m + 2, n), (m + 1, n), (m, n + 1), (m - 1, n), (m - 2, n), (m, n - 1)}. At time 0, sites are occupied with probability p. At each time step, sites that are occupied remain occupied, while sites that are not occupied become occupied if and only if three of more sites in their neig...
