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作者：Lammers, Piet
作者单位：University of Cambridge
摘要：Linde, Moore and Nordahl introduced a generalisation of the honeycomb dimer model to higher dimensions. The purpose of this article is to describe a number of structural properties of this generalised model. First, it is shown that the samples of the model are in one-to-one correspondence with the perfect matchings of a hypergraph. This leads to a generalised Kasteleyn theory: the partition function of the model equals the Cayley hyperdeterminant of the adjacency hypermatrix of the hypergraph....
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作者：Dubach, Guillaume; Peled, Yuval
作者单位：Institute of Science & Technology - Austria; New York University
摘要：We consider words G(i1) . . . G(im) involving i.i.d. complex Ginibre matrices and study tracial expressions of their eigenvalues and singular values. We show that the limit distribution of the squared singular values of every word of length m is a Fuss-Catalan distribution with parameter m + 1. This generalizes previous results concerning powers of a complex Ginibre matrix and products of independent Ginibre matrices. In addition, we find other combinatorial parameters of the word that determi...
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作者：Hammersley, William R. P.; Siska, David; Szpruch, Lukasz
作者单位：University of Edinburgh
摘要：This paper concerns the McKean-Vlasov stochastic differential equation (SDE) with common noise. An appropriate definition of a weak solution to such an equation is developed. The importance of the notion of compatibility in this definition is highlighted by a demonstration of its role in connecting weak solutions to McKean-Vlasov SDEs with common noise and solutions to corresponding stochastic partial differential equations (SPDE5). By keeping track of the dependence structure between all comp...
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作者：Krylov, N., V
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We consider Ito uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in W-d,loc(1) and the drift in L-d. We prove the unique strong solvability for any starting point and prove that, as a function of the starting point, the solutions are Holder continuous with any exponent < 1. We also prove that if we are given a sequence of coefficients converging in an appropriate sense to the original ones, then the solutions of approximating equations converge to...
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作者：Timar, Adam
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics
摘要：Answering a question of Benjamini, we present an isometry-invariant random partition of the Euclidean space R-d, d >= 3, into infinite connected indistinguishable pieces, such that the adjacency graph defined on the pieces is the 3-regular infinite tree. Along the way, it is proved that any finitely generated one-ended amenable Cayley graph can be represented in R-d as an isometry-invariant random partition of R-d to bounded polyhedra, and also as an isometry-invariant random partition of R-d ...
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作者：Corwin, Ivan; Ghosal, Promit; Hammond, Alan
作者单位：Columbia University; Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：We consider the narrow wedge solution to the Kardar-Parisi-Zhang stochastic PDE under the characteristic 3 : 2 : 1 scaling of time, space and fluctuations. We study the correlation of fluctuations at two different times. We show that, when the times are close to each other, the correlation approaches one at a power-law rate with exponent 2/3, while, when the two times are remote from each other, the correlation tends to zero at a powerlaw rate with exponent -1/3. We also prove exponential-type...
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作者：Aggarwal, Amol; Lopatto, Patrick; Marcinek, Jake
作者单位：Columbia University; Institute for Advanced Study - USA; Harvard University
摘要：We analyze statistics for eigenvector entries of heavy-tailed random symmetric matrices (also called Levy matrices) whose associated eigenvalues are sufficiently small. We show that the limiting law of any such entry is nonGaussian, given by the product of a normal distribution with another random variable that depends on the location of the corresponding eigenvalue. Although the latter random variable is typically nonexplicit, for the median eigenvector it is given by the inverse of a one-sid...
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作者：Gwynne, Ewain; Miller, Jason
作者单位：University of Cambridge
摘要：We study simple random walk on the class of random planar maps which can be encoded by a two-dimensional random walk with i.i.d.. increments or a two-dimensional Brownian motion via a mating-of-trees type bijection. This class includes the uniform infinite planar triangulation (UIPT), the infinite-volume limits of random planar maps weighted by the number of spanning trees, bipolar orientations, or Schnyder woods they admit, and the gamma-mated-CRT map for gamma is an element of (0, 2). For ea...
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作者：Hough, Robert; Son, Hyojeong
作者单位：State University of New York (SUNY) System; Stony Brook University; Washington University (WUSTL)
摘要：Sandpile dynamics are considered on graphs constructed from periodic plane and space tilings by assigning a growing piece of the tiling, either torus or open boundary conditions. A general method of obtaining the Green's function of the tiling is given, and a total variation cut-off phenomenon is demonstrated under general conditions. It is shown that the boundary condition does not affect the mixing time for planar tilings. In a companion paper, computational methods are used to demonstrate t...
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作者：Chen, Xin; Chen, Zhen-Qing; Kumagai, Takashi; Wang, Jian
作者单位：Shanghai Jiao Tong University; University of Washington; University of Washington Seattle; Kyoto University; Fujian Normal University; Fujian Normal University; Fujian Normal University
摘要：In this paper we study homogenization problem for strong Markov processes on R-d having infinitesimal generators Lf(x) = integral(Rd) (f(x + z) - f(x) - (del f(x), z)1({vertical bar z vertical bar <= 1}))k(x, z)Pi(dz) +< b(x), del f(x)>, f is an element of C-b(2)(R-d) in periodic media, where Pi is a nonnegative measure on R-d that does not charge the origin 0, satisfies f(Rd) (1 <^> vertical bar z vertical bar(2))Pi(dz) < infinity and can be singular with respect to the Lebesgue measure on R-...
