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作者：Hoi Nguyen; Tao, Terence; Van Vu
作者单位：University System of Ohio; Ohio State University; University of California System; University of California Los Angeles; Yale University
摘要：Gaps (or spacings) between consecutive eigenvalues are a central topic in random matrix theory. The goal of this paper is to study the tail distribution of these gaps in various random matrix models. We give the first repulsion bound for random matrices with discrete entries and the first super-polynomial bound on the probability that a random graph has simple spectrum, along with several applications.
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作者：Pinsky, Ross G.; Travers, Nicholas F.
作者单位：Technion Israel Institute of Technology; Indiana University System; Indiana University Bloomington
摘要：We study a random walk on which evolves in a dynamic environment determined by its own trajectory. Sites flip back and forth between two modes, p and q. R consecutive right jumps from a site in the q-mode are required to switch it to the p-mode, and L consecutive left jumps from a site in the p-mode are required to switch it to the q-mode. From a site in the p-mode the walk jumps right with probability p and left with probability , while from a site in the q-mode these probabilities are q and ...
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作者：Yogeshwaran, D.; Subag, Eliran; Adler, Robert J.
作者单位：Indian Statistical Institute; Indian Statistical Institute Bangalore; Weizmann Institute of Science; Technion Israel Institute of Technology
摘要：We consider the topology of simplicial complexes with vertices the points of a random point process and faces determined by distance relationships between the vertices. In particular, we study the Betti numbers of these complexes as the number of vertices becomes large, obtaining limit theorems for means, strong laws, concentration inequalities and central limit theorems. As opposed to most prior papers treating random complexes, the limit with which we work is in the so-called 'thermodynamic'...
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作者：Banerjee, Sayan; Kendall, Wilfrid S.
作者单位：University of Warwick
摘要：Maximal couplings are (probabilistic) couplings of Markov processes such that the tail probabilities of the coupling time attain the total variation lower bound (Aldous bound) uniformly for all time. Markovian (or immersion) couplings are couplings defined by strategies where neither process is allowed to look into the future of the other before making the next transition. Markovian couplings are typically easier to construct and analyze than general couplings, and play an important role in ma...
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作者：Sznitman, Alain-Sol
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider random interlacements on Z(d), d >= 3, when their vacant set is in a strongly percolative regime. We derive an asymptotic upper bound on the probability that the random interlacements disconnect a box of large side-length from the boundary of a larger homothetic box. As a corollary, we obtain an asymptotic upper bound on a similar quantity, where the random interlacements are replaced by the simple random walk. It is plausible, but open at the moment, that these asymptotic upper bo...
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作者：Stauffer, Alexandre
作者单位：University of Bath
摘要：We study random triangulations of the integer points [0, n](2) boolean AND Z(2), where each triangulation has probability measure with being a real parameter and denoting the sum of the length of the edges in . Such triangulations are called lattice triangulations. We construct a height function on lattice triangulations and prove that, in the whole subcritical regime , the function behaves as a Lyapunov function with respect to Glauber dynamics; that is, the function is a supermartingale. We ...
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作者：Bettinelli, Jeremie; Miermont, Gregory
作者单位：Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique; Institut Polytechnique de Paris; Ecole Polytechnique; Ecole Normale Superieure de Lyon (ENS de LYON); Institut Universitaire de France
摘要：We show that, under certain natural assumptions, large random plane bipartite maps with a boundary converge after rescaling to a one-parameter family of random metric spaces homeomorphic to the closed unit disk of , the space being called the Brownian disk of perimeter L and unit area. These results can be seen as an extension of the convergence of uniform plane quadrangulations to the Brownian map, which intuitively corresponds to the limit case where . Similar results are obtained for maps f...
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作者：Georgiou, Nicos; Rassoul-Agha, Firas; Seppalainen, Timo
作者单位：University of Sussex; Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison
摘要：We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, outside of the class of exactly solvable models. Stationary cocycles are constructed for this percolation model from queueing fixed points. These cocycles serve as boundary conditions for stationary last-passage percolation, solve variational formulas that characterize limit shapes, and yield existence of Busemann functions in directions wher...
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作者：Bao, Zhigang; Erdos, Laszlo
作者单位：Institute of Science & Technology - Austria
摘要：We consider Hermitian random matrices H consisting of blocks of size . The matrix elements are i.i.d. within the blocks, close to a Gaussian in the four moment matching sense, but their distribution varies from block to block to form a block-band structure, with an essential band width M. We show that the entries of the Green's function satisfy the local semicircle law with spectral parameter down to the real axis for any , using a combination of the supersymmetry method inspired by Shcherbina...
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作者：Soo, Terry
作者单位：University of Kansas
摘要：In the simple case of a Bernoulli shift on two symbols, zero and one, by permuting the symbols, it is obvious that any two equal entropy shifts are isomorphic. We show that the isomorphism can be realized by a factor that maps a binary sequence to another that is coordinatewise smaller than or equal to the original sequence.
