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作者：Gnewuch, Michael; Hebbinghaus, Nils
作者单位：University Osnabruck; University of Kiel
摘要：We introduce a class of gamma-negatively dependent random samples. We prove that this class includes, apart from Monte Carlo samples, in particular Latin hypercube samples and Latin hypercube samples padded by Monte Carlo. For a gamma-negatively dependent N-point sample in dimension d we provide probabilistic upper bounds for its star discrepancy with explicitly stated dependence on N, d, and gamma. These bounds generalize the probabilistic bounds for Monte Carlo samples from Heinrich et al. (...
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作者：Athreya, Siva; den Hollander, Frank; Rollin, Adrian
作者单位：Indian Statistical Institute; Indian Statistical Institute Bangalore; Leiden University; Leiden University - Excl LUMC; National University of Singapore
摘要：The goal of this paper is to construct a natural class of graphon-valued processes arising from population genetics. We consider finite populations where individuals carry one of finitely many genetic types and change type according to Fisher-Wright resampling. At any time, each pair of individuals is linked by an edge with a probability that is given by a type-connection matrix, whose entries depend on the current types of the two individuals and on the current empirical type distribution of ...
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作者：Janson, Svante; Warnke, Lutz
作者单位：Uppsala University; University System of Georgia; Georgia Institute of Technology
摘要：We study the following preferential attachment variant of the classical Erd os-Renyi random graph process. Starting with an empty graph on n vertices, new edges are added one-by-one, and each time an edge is chosen with probability roughly proportional to the product of the current degrees of its endpoints (note that the vertex set is fixed). We determine the asymptotic size of the giant component in the supercritical phase, confirming a conjecture of Pittel from 2010. Our proof uses a simple ...
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作者：Fang, Xiao; Koike, Yuta
作者单位：Chinese University of Hong Kong; University of Tokyo
摘要：We obtain explicit error bounds for the d-dimensional normal approximation on hyperrectangles for a random vector that has a Stein kernel, or admits an exchangeable pair coupling, or is a nonlinear statistic of independent random variables or a sum of n locally dependent random vectors. We assume the approximating normal distribution has a nonsingular covariance matrix. The error bounds vanish even when the dimension d is much larger than the sample size n. We prove our main results using the ...
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作者：Chen, Wei-Kuo; Handschy, Madeline; Lerman, Gilad
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Consider a spiked random tensor obtained as a mixture of two components: noise in the form of a symmetric Gaussian p-tensor for p >= 3 and signal in the form of a symmetric low-rank random tensor. The latter is defined as a linear combination of k independent symmetric rank-one random tensors, referred to as spikes, with weights referred to as signal-to-noise ratios (SNRs). The entries of the vectors that determine the spikes are i.i.d. sampled from general probability distributions supported ...
