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作者：Chen, Wei-Kuo; Gamarnik, David; Panchenko, Dmitry; Rahman, Mustazee
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Toronto; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：We show that in random K-uniform hypergraphs of constant average degree, for even K >= 4, local algorithms defined as factors of i.i.d. can not find nearly maximal cuts, when the average degree is sufficiently large. These algorithms have been used frequently to obtain lower bounds for the max-cut problem on random graphs, but it was not known whether they could be successful in finding nearly maximal cuts. This result follows from the fact that the overlap of any two nearly maximal cuts in su...
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作者：Borodin, Alexei; Gorin, Vadim
作者单位：Massachusetts Institute of Technology (MIT); Kharkevich Institute for Information Transmission Problems of the RAS
摘要：A stochastic telegraph equation is defined by adding a random inhomogeneity to the classical (second-order linear hyperbolic) telegraph differential equation. The inhomogeneities we consider are proportional to the two-dimensional white noise, and solutions to our equation are two-dimensional random Gaussian fields. We show that such fields arise naturally as asymptotic fluctuations of the height function in a certain limit regime of the stochastic six-vertex model in a quadrant. The correspon...
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作者：Lambert, Gaultier; Ledoux, Michel; Webb, Christian
作者单位：University of Zurich; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Institut Universitaire de France; Aalto University
摘要：We present a new approach, inspired by Stein's method, to prove a central limit theorem (CLT) for linear statistics of beta-ensembles in the one-cut regime. Compared with the previous proofs, our result requires less regularity on the potential and provides a rate of convergence in the quadratic Kantorovich or Wasserstein-2 distance. The rate depends both on the regularity of the potential and the test functions, and we prove that it is optimal in the case of the Gaussian Unitary Ensemble (GUE...
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作者：Gamarnik, David; Ramanan, Kavita
作者单位：Massachusetts Institute of Technology (MIT); Brown University
摘要：We formulate a continuous version of the well-known discrete hardcore (or independent set) model on a locally finite graph, parameterized by the so-called activity parameter lambda > 0. In this version the state or spin value x(u) of any node u of the graph lies in the interval [0, 1], the hardcore con- straint x(u) + x(v) <= 1 is satisfied for every edge (u, v) of the graph, and the space of feasible configurations is given by a convex polytope. When the graph is a regular tree, we show that ...
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作者：Pitman, Jim; Tang, Wenpin
作者单位：University of California System; University of California Berkeley
摘要：Motivated by recent studies of large Mallows(q) permutations, we propose a class of random permutations of N+ and of Z, called regenerative permutations. Many previous results of the limiting Mallows(q) permutations are recovered and extended. Three special examples: blocked permutations, p-shifted permutations and p-biased permutations are studied.
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作者：Maples, Kenneth; Najnudel, Joseph; Nikeghbali, Ashkan
作者单位：University of Zurich; University System of Ohio; University of Cincinnati
摘要：It is known that a unitary matrix can be decomposed into a product of complex reflections, one for each dimension, and that these reflections are independent and uniformly distributed on the space where they live if the initial matrix is Haar-distributed. If we take an infinite sequence of such reflections, and consider their successive products, then we get an infinite sequence of unitary matrices of increasing dimension, all of them following the circular unitary ensemble. In this coupling, ...
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作者：Chen, Le; Huang, Jingyu
作者单位：Nevada System of Higher Education (NSHE); University of Nevada Las Vegas; Utah System of Higher Education; University of Utah
摘要：We establish the strong comparison principle and strict positivity of solutions to the following nonlinear stochastic heat equation on R-d (partial derivative/partial derivative t - 1/2 Delta)u(t, x) = rho(u(t , x)) (M) over dot (t , x), for measure-valued initial data, where (M) over dot is a spatially homogeneous Gaussian noise that is white in time and rho is Lipschitz continuous. These results are obtained under the condition that integral(Rd) (1 + vertical bar xi vertical bar(2))(alpha-1)...
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作者：Ghoussoub, Nassif; Kim, Young-Heon; Lim, Tongseok
作者单位：University of British Columbia; Korea Institute for Advanced Study (KIAS); ShanghaiTech University
摘要：Given two probability measures mu and nu in convex order on R-d, we study the profile of one-step martingale plans pi on R-d x R-d that optimize the expected value of the modulus of their increment among all martingales having mu and nu as marginals. While there is a great deal of results for the real line (i.e., when d = 1), much less is known in the richer and more delicate higher-dimensional case that we tackle in this paper. We show that many structural results can be obtained, provided th...
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作者：Rhodes, Remi; Vargas, Vincent
作者单位：Aix-Marseille Universite; Universite PSL; Ecole Normale Superieure (ENS); Universite PSL; Ecole Normale Superieure (ENS)
摘要：In this short note we derive a precise tail expansion for Gaussian multiplicative chaos (GMC) associated to the 2d Gaussian Free Fiedl (GFF) on the unit disk with zero average on the unit circle (and variants). More specifically, we show that to first order the tail is a constant times an inverse power with an explicit value for the tail exponent as well as an explicit value for the constant in front of the inverse power; we also provide a second order bound for the tail expansion. The main in...
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作者：Kenyon, Richard
作者单位：Brown University
摘要：We generalize the uniform spanning tree to construct a family of determinantal measures on essential spanning forests on periodic planar graphs in which every component tree is bi-infinite. Like the uniform spanning tree, these measures arise naturally from the Laplacian on the graph. More generally, these results hold for the massive Laplacian determinant which counts rooted spanning forests with weight M per finite component. These measures typically have a form of conformal invariance, unli...
