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作者：Dolega, Maciej; Sniady, Piotr
作者单位：Adam Mickiewicz University; University of Wroclaw; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：We introduce a large class of random Young diagrams which can be regarded as a natural one-parameter deformation of some classical Young diagram ensembles; a deformation which is related to Jack polynomials and Jack characters. We show that each such a random Young diagram converges asymptotically to some limit shape and that the fluctuations around the limit are asymptotically Gaussian.
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作者：Duminil-Copin, Hugo; Raoufi, Aran; Tassion, Vincent
作者单位：University of Geneva; Universite Paris Saclay; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We prove that for Voronoi percolation on Rd(d2), there exists pc=pc(d)(0,1) such thatfor p0 such that Pp[0connected to distancen]exp(-cpn),there exists c>0 such that for p>pc,Pp[0connected to infinity]c(p-pc). For dimension 2, this result offers a new way of showing that pc(2)=1/2. This paper belongs to a series of papers using the theory of algorithms to prove sharpness of the phase transition; see [10, 11].
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作者：Fan, Zhou; Montanari, Andrea
作者单位：Stanford University; Stanford University
摘要：We study an inner-product kernel random matrix model, whose empirical spectral distribution was shown by Xiuyuan Cheng and Amit Singer to converge to a deterministic measure in the large n and p limit. We provide an interpretation of this limit measure as the additive free convolution of a semicircle law and a Marchenko-Pastur law. By comparing the tracial moments of this matrix to an additive deformation of a Wigner matrix, we establish that for odd kernel functions, the spectral norm of this...
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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...
