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作者：Viklund, Fredrik Johansson; Rohde, Steffen; Wong, Carto
作者单位：Columbia University; University of Washington; University of Washington Seattle
摘要：We prove that for almost every Brownian motion sample, the corresponding SLE curves parameterized by capacity exist and change continuously in the supremum norm when varies in the interval , where . We estimate the -dependent modulus of continuity of the curves and also give an estimate on the modulus of continuity for the supremum norm change with .
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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：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：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.
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作者：Bertini, Lorenzo; Giacomin, Giambattista; Poquet, Christophe
作者单位：Sapienza University Rome; Universite Paris Cite; Universite Paris Cite; Sorbonne Universite
摘要：We consider the natural Langevin dynamics which is reversible with respect to the mean-field plane rotator (or classical spin XY) measure. It is well known that this model exhibits a phase transition at a critical value of the interaction strength parameter K, in the limit of the number N of rotators going to infinity. A Fokker-Planck PDE captures the evolution of the empirical measure of the system as N ->infinity, at least for finite times and when the empirical measure of the system at time...
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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：The circular law asserts that the spectral measure of eigenvalues of rescaled random matrices without symmetry assumption converges to the uniform measure on the unit disk. We prove a local version of this law at any point away from the unit circle. More precisely, if for arbitrarily small , the circular law is valid around up to scale for any under the assumption that the distributions of the matrix entries satisfy a uniform subexponential decay condition.
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作者：Dalalyan, Arnak; Ingster, Yuri; Tsybakov, Alexandre B.
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Saint Petersburg State Electrotechnical University
摘要：We consider a general nonparametric regression model called the compound model. It includes, as special cases, sparse additive regression and nonparametric (or linear) regression with many covariates but possibly a small number of relevant covariates. The compound model is characterized by three main parameters: the structure parameter describing the macroscopic form of the compound function, the microscopic sparsity parameter indicating the maximal number of relevant covariates in each compon...
