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作者：Nolin, Pierre
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Universite Paris Saclay
摘要：We study gradient percolation for site percolation on the triangular lattice. This is a percolation model where the percolation probability depends linearly on the location of the site. We prove the results predicted by physicists for this model. More precisely, we describe the fluctuations of the interfaces around their (straight) scaling limits, and the expected and typical lengths of these interfaces. These results build on the recent results for critical percolation on this lattice by Smir...
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作者：Blachere, Sebastien; Haissinsky, Peter; Mathieu, Pierre
作者单位：Aix-Marseille Universite
摘要：We study asymptotic proper-ties of the Green metric associated with transient random walks on countable groups. We prove that the rate of escape of the random walk computed in the Green metric equals its asymptotic entropy. The proof relies on integral representations of both quantities with the extended Martin kernel. In the case of finitely generated groups, where this result is known (Benjamini and Peres [Probab. Theory Related Fields 98 (1994) 91-112]), we give an alternative proof relying...
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作者：Zhan, Dapeng
作者单位：Yale University
摘要：We define a family of stochastic Loewner evolution-type processes in finitely connected domains, which are called continuous LERW (loop-erased random walk). A continuous LERW describes a random curve in a finitely connected domain that starts from a prime end and ends at a certain target set, which could be an interior point, or a prime end, or a side arc. It is defined using the usual chordal Loewner equation with the driving function being root 2B(t) plus a drift term. The distributions of c...
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作者：Berger, Noam
作者单位：University of California System; University of California Los Angeles
摘要：We show that random walk in uniformly elliptic i.i.d. environment in dimension >= 5 has at most one non zero limiting velocity. In particular this proves a law of large numbers in the distributionally symmetric case and establishes connections between different conjectures.
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作者：Haas, Benedicte; Miermont, Gregory; Pitman, Jim; Winkel, Matthias
作者单位：Universite PSL; Universite Paris-Dauphine; Universite Paris Saclay; University of California System; University of California Berkeley; University of Oxford
摘要：Given any regularly varying dislocation we measure, We identify a natural self-similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As an application, we obtain continuum random tree limits of Aldous's beta-splitting models and Ford's alpha models for phylogenetic trees. limits of Aldous's beta-splitting, models and Ford's alpha models for phylogenetic trees. This confirms in a strong way that the whole trees row at the same speed as the mean heig...
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作者：Sly, Allan; Heyde, Chris
作者单位：University of California System; University of California Berkeley; Australian National University; Columbia University
摘要：We consider functionals of long-range dependent Gaussian sequences with infinite variance and obtain nonstandard limit theorems. When the long-range dependence is strong enough, the limit is a Hermite process, while for weaker long-range dependence, the limit is alpha-stable Levy motion. For the critical value of the long-range dependence parameter, the limit is a sum of a Hermite process and alpha-stable Levy motion.
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作者：Singh, Arvind
作者单位：Sorbonne Universite
摘要：We consider a diffusion process X in a random Levy potential V which is a solution of the informal stochastic differential equation {dX(t) = d beta(t)-1/2V '(X-t)dt, X-0 = 0, (beta B. M. independent of V). We study the rate of convergence when the diffusion is transient under the assumption that the Levy process V does not possess positive jumps. We generalize the previous results of Hu-Shi-Yor for drifted Brownian potentials. In particular, we prove a conjecture of Carmona: provided that ther...
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作者：El-Dakkak, Omar; Peccati, Giovanni
作者单位：Sorbonne Universite
摘要：Let X = (X(1), X(2),...) be a nondeterministic infinite exchangeable sequence with values in {0, 1}. We show that X is Hoeffding decomposable if, and only if, X is either an i.i.d. sequence or a Polya sequence. This completes the results established in Peccati [Ann. Probab. 32 (2004) 1796-1829]. The proof uses several combinatorial implications of the correspondence between Hoeffding decomposability and weak independence. Our results must be compared with previous Characterizations of i.i.d. a...
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作者：Guan, Qing-Yang; Winkel, Matthias
作者单位：Chinese Academy of Sciences; University of Oxford
摘要：Stochastic Loewner evolutions (SLE) with a multiple root kappa B of Brownian motion B as driving process are random planar curves (if kappa < 4) or growing compact sets generated by a curve (if kappa > 4). We consider here more general Levy processes as driving processes and obtain evolutions expected to look like random trees or compact sets generated by trees, respectively. We show that when the driving force is of the form root kappa B + theta(1/alpha) S for a symmetric a-stable Levy proces...
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作者：Caravenna, Francesco; Deuschel, Jean-Dominique
作者单位：University of Padua; Technical University of Berlin
摘要：We consider a random field phi : {1,..., N} -> R as a model fora linear chain attracted to the defect line phi = 0. that is, the x-axis. The free law of the field is specified by the density exp(-Sigma(i) V(Delta phi(i))) with respect to the Lebesgue measure on R(N), where Delta is the discrete Laplacian and we allow for a very large class of potentials V(.). The interaction with the defect line is introduced by giving the field a reward epsilon >= 0 each time it touches the x-axis. We call th...
