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作者：Bourgade, Paul; Yau, Horng-Tzer; Yin, Jun
作者单位：Harvard University; University of Wisconsin System; University of Wisconsin Madison
摘要：In the first part of this article (Bourgade et al. arXiv:1206.1449, 2012), we proved a local version of the circular law up to the finest scale for non-Hermitian random matrices at any point with for any independent of the size of the matrix. Under the main assumption that the first three moments of the matrix elements match those of a standard Gaussian random variable after proper rescaling, we extend this result to include the edge case . Without the vanishing third moment assumption, we pro...
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作者：Goldenshluger, A.; Lepski, O.
作者单位：University of Haifa; Aix-Marseille Universite
摘要：We address the problem of adaptive minimax density estimation on with -loss on the anisotropic Nikol'skii classes. We fully characterize behavior of the minimax risk for different relationships between regularity parameters and norm indexes in definitions of the functional class and of the risk. In particular, we show that there are four different regimes with respect to the behavior of the minimax risk. We develop a single estimator which is (nearly) optimal in order over the complete scale o...
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作者：Petrov, Leonid
作者单位：Northeastern University; Kharkevich Institute for Information Transmission Problems of the RAS
摘要：A Gelfand-Tsetlin scheme of depth N is a triangular array with m integers at level m, m = 1, ... , N, subject to certain interlacing constraints. We study the ensemble of uniformly random Gelfand-Tsetlin schemes with arbitrary fixed Nth row. We obtain an explicit double contour integral expression for the determinantal correlation kernel of this ensemble (and also of its q-deformation). This provides new tools for asymptotic analysis of uniformly random lozenge tilings of polygons on the trian...
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作者：Kabluchko, Zakhar; Klimovsky, Anton
作者单位：Ulm University; Leiden University; Leiden University - Excl LUMC
摘要：The partition function of the random energy model at inverse temperature is a sum of random exponentials , where are independent real standard normal random variables (=random energies), and . We study the large N limit of the partition function viewed as an analytic function of the complex variable . We identify the asymptotic structure of complex zeros of the partition function confirming and extending predictions made in the theoretical physics literature. We prove limit theorems for the ra...
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作者：Gamarnik, David
作者单位：Massachusetts Institute of Technology (MIT)
摘要：The paper is devoted to the problem of establishing right-convergence of sparse random graphs. This concerns the convergence of the logarithm of number of homomorphisms from graphs or hyper-graphs to some target graph . The theory of dense graph convergence, including random dense graphs, is now well understood (Borgs et al. in Ann Math 176:151-219, 2012; Borgs et al. in Adv Math 219:1801-1851, 2008; Chatterjee and Varadhan in Eur J Comb 32:1000-1017, 2011; Lovasz and Szegedy in J Comb Theory ...
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作者：Barbour, A. D.; Kowalski, E.; Nikeghbali, A.
作者单位：University of Zurich; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：In this paper, we consider approximating expansions for the distribution of integer valued random variables, in circumstances in which convergence in law (without normalization) cannot be expected. The setting is one in which the simplest approximation to the -th random variable is by a particular member of a given family of distributions, whose variance increases with . The basic assumption is that the ratio of the characteristic function of to that of converges to a limit in a prescribed fas...
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作者：Lacoin, Hubert
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：In this paper, we study the abundance of self-avoiding paths of a given length on a supercritical percolation cluster on . More precisely, we count , the number of self-avoiding paths of length on the infinite cluster starting from the origin (which we condition to be in the cluster). We are interested in estimating the upper growth rate of , , which we call the connective constant of the dilute lattice. After proving that this connective constant is a.s. non-random, we focus on the two-dimens...
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作者：Espinasse, T.; Gamboa, F.; Loubes, J-M.
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：In this paper, using spectral theory of Hilbertian operators, we study a special class of Gaussian processes indexed by graphs. We extend Whittle maximum likelihood estimation of the parameters for the corresponding spectral density and show their asymptotic optimality.
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作者：Grimmett, Geoffrey R.; Manolescu, Ioan
作者单位：University of Cambridge
摘要：In an investigation of percolation on isoradial graphs, we prove the criticality of canonical bond percolation on isoradial embeddings of planar graphs, thus extending celebrated earlier results for homogeneous and inhomogeneous square, triangular, and other lattices. This is achieved via the star-triangle transformation, by transporting the box-crossing property across the family of isoradial graphs. As a consequence, we obtain the universality of these models at the critical point, in the se...
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作者：Austin, Tim; Panchenko, Dmitry
作者单位：New York University; Texas A&M University System; Texas A&M University College Station
摘要：We consider random arrays indexed by the leaves of an infinitary rooted tree of finite depth, with the distribution invariant under the rearrangements that preserve the tree structure. We call such arrays hierarchically exchangeable and prove that they satisfy an analogue of de Finetti's theorem. We also prove a more general result for arrays indexed by several trees, which includes a hierarchical version of the Aldous-Hoover representation.
