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作者：Cerf, Raphael; Dembin, Barbara
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider the standard model of i.i.d. first passage percolation on Z(d) given a distribution G on [0, +infinity] (-infinity is allowed). When G([0, +infinity)) > p(c) (d), it is known that the time constant mu(G) exists. We are interested in the regularity properties of the map G bar right arrow mu(G). We first study the specific case of distributions of the form G(p) = p delta(1) + (1 - p)delta(infinity) for p > p(c) (d). In this case, the travel time between two points is equal to the len...
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作者：Bjornberg, Jakob; Curien, Nicolas; Stefansson, Sigurdur Orn
作者单位：Chalmers University of Technology; University of Gothenburg; Universite Paris Saclay; Institut Universitaire de France; University of Iceland
摘要：We introduce a new familiy of random compact metric spaces S-alpha for alpha is an element of (1, 2), which we call stable shredded spheres. They are constructed from excursions of alpha-stable Levy processes on [0, 1] possessing no negative jumps. Informally, viewing the graph of the Levy excursion in the plane, each jump of the process is cut open and replaced by a circle, and then all points on the graph at equal height, which are not separated by a jump, are identified. We show that the sh...
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作者：Riera, Armand
作者单位：Universite Paris Saclay
摘要：We consider the model of the Brownian plane, which is a pointed non-compact random metric space with the topology of the complex plane. The Brownian plane can be obtained as the scaling limit in distribution of the uniform infinite planar triangulation or the uniform infinite planar quadrangulation and is conjectured to be the universal scaling limit of many others random planar lattices. We establish sharp bounds on the probability of having a short cycle separating the ball of radius r cente...
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作者：Pimentel, Leandro P. R.
作者单位：Universidade Federal do Rio de Janeiro
摘要：In this article, we consider the KPZ fixed point starting from a two-sided Brownian motion with an arbitrary diffusion coefficient. We apply the integration by parts formula from Malliavin calculus to establish a key relation between the two-point (correlation) function of the spatial derivative process and the location of the maximum of an Airy process plus Brownian motion minus a parabola. Integration by parts also allows us to deduce the density of this location in terms of the second deriv...
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作者：Giunti, Arianna; Gu, Chenlin; Mourrat, Jean-Christophe
作者单位：Imperial College London; Universite PSL; Ecole Normale Superieure (ENS); New York University
摘要：For a class of interacting particle systems in continuous space, we show that finite-volume approximations of the bulk diffusion matrix converge at an algebraic rate. The models we consider are reversible with respect to the Poisson measures with constant density, and are of nongradient type. Our approach is inspired by recent progress in the quantitative homogenization of elliptic equations. Along the way, we develop suitable modifications of the Caccioppoli and multiscale Poincare inequaliti...
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作者：Kenyon, Richard; Pohoata, Cosmin
作者单位：Yale University
摘要：Given a graph g and collection of subgraphs T (called tiles), we consider covering g with copies of tiles in T so that each vertex v is an element of( )G is covered with a predetermined multiplicity. The multinomial tiling model is a natural probability measure on such configurations (it is the uniform measure on standard tilings of the corresponding blow-up of G). In the limit of large multiplicities, we compute the asymptotic growth rate of the number of multinomial tilings. We show that the...
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作者：Budzinski, Thomas; Lehericy, Thomas
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); University of Zurich
摘要：We study the simple random walk on the Uniform Infinite Half-Plane Map, which is the local limit of critical Boltzmann planar maps with a large and simple boundary. We prove that the simple random walk is recurrent, and that the resistance between the root and the boundary of the hull of radius r is at least of order log r . This resistance bound is expected to be sharp, and is better than those following from previous proofs of recurrence for nonbounded-degree planar maps models. Our main too...
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作者：Hermon, Jonathan; Li, Shuangping; Yao, Dong; Zhang, Lingfu
作者单位：University of British Columbia; Princeton University; Jiangsu Normal University; Princeton University
摘要：In this paper, we consider coalescing random walks on a general connected graph G = (V, E). We set up a unified framework to study the leading order of the decay rate of P-t , the expectation of the fraction of occupied sites at time t, particularly for the 'Big Bang' regime where t << t(coal) :=E(inf{s : There is only one particle at time s}). Our results show that P-t satisfies certain 'mean-field behaviors' if the graphs satisfy certain 'transience-like' conditions. We apply this framework ...
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作者：Goswami, Subhajit; Rodriguez, Pierre-Francois; Severo, Franco
作者单位：Tata Institute of Fundamental Research (TIFR); Imperial College London; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider the Gaussian free field phi on Z(d), for d >= 3, and give sharp bounds on the probability that the radius of a finite cluster in the excursion set {phi >= h} exceeds a large value N for any height h not equal h(*), where h(*) refers to the corresponding percolation critical parameter. In dimension 3, we prove that this probability is subexponential in N and decays as exp{-pi/6 (h - h(*))(2) N/logN} as N -> infinity to principal exponential order. When d >= 4, we prove that these ta...
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作者：Dauvergne, Duncan; Sarkar, Sourav; Virag, Balint
作者单位：University of Toronto; University of Cambridge
摘要：We show that geodesics in the directed landscape have 3/2-variation and that weight functions along the geodesics have cubic variation. We show that the geodesic and its landscape environment around an interior point have a small-scale limit. This limit is given in terms of the directed landscape with Brownian-Bessel boundary conditions. The environments around different interior points are asymptotically independent. We give tail bounds with optimal exponents for geodesic and weight function ...
