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作者：Duminil-Copin, Hugo; Lis, Marcin
作者单位：University of Geneva; University of Vienna
摘要：We relate the planar random current representation introduced by Griffiths, Hurst and Sherman to the dimer model. More precisely, we provide a measure-preserving map between double random currents (obtained as the sum of two independent random currents) on a planar graph and dimers on an associated bipartite graph. We also define a nesting field for the double random current, which, under this map, corresponds to the height function of the dimer model. As applications, we provide an alternativ...
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作者：Gerencser, Mate; Hairer, Martin
作者单位：Institute of Science & Technology - Austria; University of Warwick
摘要：We study spaces of modelled distributions with singular behaviour near the boundary of a domain that, in the context of the theory of regularity structures, allow one to give robust solution theories for singular stochastic PDEs with boundary conditions. The calculus of modelled distributions established in Hairer (Invent Math 198(2):269-504, 2014. 10.1007/s00222-014-0505-4) is extended to this setting. We formulate and solve fixed point problems in these spaces with a class of kernels that is...
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作者：Yao, Chang-Long
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：We study Bernoulli first-passage percolation (FPP) on the triangular lattice in which sites have 0 and 1 passage times with probability p and 1- p, respectively. Denote by C8 the infinite cluster with 0-time sites when p > pc, where pc = 1/2 is the critical probability. Denote by T (0, C8) the passage time from the origin 0 to C8. First we obtain explicit limit theorem for T (0, C8) as p pc. The proof relies on the limit theorem in the critical case, the critical exponent for correlation lengt...
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作者：Holroyd, Alexander E.; Marcovici, Irene; Martin, James B.
作者单位：Universite de Lorraine; University of Oxford
摘要：Let each site of the square lattice Z2 be independently assigned one of three states: a trap with probability p, a target with probability q, and open with probability 1-p-q, where 0<1. Consider the following game: a token starts at the origin, and two players take turns to move, where a move consists of moving the token from its current site x to either x+(0,1) or x+(1,0). A player who moves the token to a trap loses the game immediately, while a player who moves the token to a target wins th...
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作者：Chapuy, Guillaume
作者单位：Universite Paris Cite
摘要：We study the masses of the two cells in a Voronoi tessellation of the Brownian surface of genus g0 centered on two uniform random points. Making use of classical bijections and asymptotic estimates for maps of fixed genus, we relate the second moment of these random variables to the Painleve-I equation satisfied by the double scaling limit of the one-matrix model, or equivalently to the tg-recurrence satisfied by the constants tg driving the asymptotic number of maps of genus g0. This raises t...
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作者：Brunel, Victor-Emmanuel
作者单位：Massachusetts Institute of Technology (MIT)
摘要：Tukey's halfspace depth has attracted much interest in data analysis, because it is a natural way of measuring the notion of depth relative to a cloud of points or, more generally, to a probability measure. Given an i.i.d. sample, we investigate the concentration of upper level sets of the Tukey depth relative to that sample around their population version. We show that under some mild assumptions on the underlying probability measure, concentration occurs at a parametric rate and we deduce mo...
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作者：Filmus, Yuval; Mossel, Elchanan
作者单位：Technion Israel Institute of Technology; Massachusetts Institute of Technology (MIT)
摘要：In a recent work with Kindler and Wimmer we proved an invariance principle for the slice for low-influence, low-degree harmonicmultilinear polynomials (a polynomial in x1,..., xn is harmonic if it is annihilated by n i=1.. xi). Here we provide an alternative proof for general low-degree harmonicmultilinear polynomials, with no constraints on the influences. We show that any real-valued harmonic multilinear polynomial on the slice whose degree is o(v n) has approximately the same distribution u...
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作者：Heydenreich, Markus; van der Hofstad, Remco
作者单位：Vrije Universiteit Amsterdam; Eindhoven University of Technology
摘要：In [3, Theorem 1.2], we claim that the maximal cluster for critical percolation on the high-dimensional torus is non-concentrated. This proof contains an error. In this note, we replace this statement by a conditional statement instead.
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作者：Zhan, Dapeng
作者单位：Michigan State University
摘要：We make use of the fact that a two-sided whole-plane Schramm-Loewner evolution (SLE kappa) curve gamma for kappa is an element of (0, 8) from infinity to infinity through 0 may be parametrized by its d-dimensional Minkowski content, where d = 1 + kappa/8, and become a self-similar process of index 1/d with stationary increments. We prove that such gamma is locally alpha-Holder continuous for any alpha < 1/d. In the case kappa is an element of (0, 4], we show that gamma is not locally 1/d-Holde...
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作者：Cerrai, Sandra; Freidlin, Mark
作者单位：University System of Maryland; University of Maryland College Park
摘要：Fast advection asymptotics for a stochastic reaction-diffusion-advection equation are studied in this paper. To describe the asymptotics, we introduce a new class of SPDEs defined on a graph, corresponding to the stream function of the underlying incompressible flow. We prove that, as the advection term becomes faster and faster, the solution of the stochastic reaction-diffusion-advection equation on the plane converges in a suitable sense to the solution of such an SPDE defined on the graph. ...
