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作者：Le Gall, Jean-Francois; Lehericy, Thomas
作者单位：Universite Paris Saclay
摘要：We study geometric properties of the infinite random lattice called the uniform infinite planar quadrangulation or UIPQ. We establish a precise form of a conjecture of Krikun stating that the minimal size of a cycle that separates the ball of radius R centered at the root vertex from infinity grows linearly in R. As a consequence, we derive certain isoperimetric bounds showing that the boundary size of any simply connected set A consisting of a finite union of faces of the UIPQ and containing ...
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作者：Tang, Pengfei
作者单位：Indiana University System; Indiana University Bloomington
摘要：We prove that the heavy clusters are indistinguishable for Bernoulli percolation on quasi-transitive nonunimodular graphs. As an application, we show that the uniqueness threshold of any quasi-transitive graph is also the threshold for connectivity decay. This resolves a question of Lyons and Schramm (Ann. Probab.27 (1999) 1809-1836) in the Bernoulli percolation case and confirms a conjecture of Schonmann (Comm. Math. Phys. 219 (2001) 271-322). We also prove that every infinite cluster of Bern...
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作者：Kramkov, Dmitry; Pulido, Sergio
作者单位：Carnegie Mellon University; Universite Paris Saclay; Ecole Nationale Superieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE)
摘要：Let psi be a multidimensional random variable. We show that the set of probability measures Q such that the Q-martingale S-t(Q) = E-Q[psi vertical bar F-t] has the Martingale Representation Property (MRP) is either empty or dense in L-infinity-norm. The proof is based on a related result involving analytic fields of terminal conditions (psi (x))(x)(is an element of U) and probability measures (Q(x))(x)(is an element of U) over an open set U. Namely, we show that the set of points x is an eleme...
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作者：Martineau, Sebastien; Severo, Franco
作者单位：Universite Paris Saclay; Universite Paris Saclay
摘要：We answer a question of Benjamini and Schramm by proving that under reasonable conditions, quotienting a graph strictly increases the value of its percolation critical parameter p(c). More precisely, let G = (V, E) be a quasi-transitive graph with p(c) (G) < 1, and let G be a nontrivial group that acts freely on V by graph automorphisms. Assume that H := G/G is quasi-transitive. Then one has p(c) (G) < P-c (H). We provide results beyond this setting: we treat the case of general covering maps ...
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作者：Giunti, Arianna; Gu, Yu; Mourrat, Jean-Christophe
作者单位：University of Bonn; Carnegie Mellon University; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
摘要：We show a diffusive upper bound on the transition probability of a tagged particle in the symmetric simple exclusion process. The proof relies on optimal spectral gap estimates for the dynamics in finite volume, which are of independent interest. We also show off-diagonal estimates of Came-Varopoulos type.
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作者：Martinelli, Fabio; Toninelli, Cristina
作者单位：Roma Tre University; Centre National de la Recherche Scientifique (CNRS)
摘要：Recent years have seen a great deal of progress in our understanding of bootstrap percolation models, a particular class of monotone cellular automata. In the two-dimensional lattice Z(2), there is now a quite satisfactory understanding of their evolution starting from a random initial condition, with a strikingly beautiful universality picture for their critical behavior. Much less is known for their nonmonotone stochastic counterpart, namely kinetically constrained models (KCM). In KCM, each...
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作者：Bally, Vlad; Caramellino, Lucia
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); University of Rome Tor Vergata; University of Rome Tor Vergata
摘要：The goal of this paper is to estimate the total variation distance between two general stochastic polynomials. As a consequence, one obtains an invariance principle for such polynomials. This generalizes known results concerning the total variation distance between two multiple stochastic integrals on one hand, and invariance principles in Kolmogorov distance for multilinear stochastic polynomials on the other hand. As an application, we first discuss the asymptotic behavior of U-statistics as...
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作者：Miller, Jason; Sheffield, Scott
作者单位：University of Cambridge; Massachusetts Institute of Technology (MIT)
摘要：Let h be an instance of the GFF. Fix kappa is an element of (0, 4) and chi = 2//root kappa - root kappa/2. Recall that an imaginary geometry ray is a flow line of e(i(h/chi+theta)) that looks locally like SEE kappa. The light cone with parameter theta is an element of [0, pi] is the set of points reachable from the origin by a sequence of rays with angles in [-theta/2, theta/2]. It is known that when theta = 0, the light cone looks like SLE kappa, and when = theta = pi looks like the range of ...
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作者：Chen, Xian; Ma, Zhi-Ming; Peng, Xue
作者单位：Xiamen University; Sichuan University
摘要：For a given quasi-regular positivity preserving coercive form, we construct a family of (sigma-finite) distribution flows associated with the semigroup of the form. The canonical cadlag process equipped with the distribution flows behaves like a strong Markov process. Moreover, employing distribution flows we can construct optional measures and establish Revuz correspondence between additive functionals and smooth measures. The results obtained in this paper will enable us to perform a kind of...
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作者：Guerra Aguilar, Enrique
作者单位：Pontificia Universidad Catolica de Chile
摘要：We prove a ballistic strong law of large numbers and an invariance principle for random walks in strong mixing environments, under condition (T) of Sznitman (cf. Ann. Probab. 29 (2001) 724-765). This weakens for the first time Kalikow's ballisticity assumption on mixing environments and proves the existence of arbitrary finite order moments for the approximate regeneration time of F. Comets and O. Zeitouni (Israel J. Math. 148 (2005) 87-113). The main technical tool in the proof is the introdu...
