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作者：Atar, Rami; Castiel, Eyal; Reiman, Martin I.
作者单位：Technion Israel Institute of Technology; Columbia University
摘要：The standard setting for studying parallel server systems (PSS) at the diffusion scale is based on the heavy traffic condition (HTC), which assumes that the underlying static allocation linear program (LP) is critical and has a unique solution. This solution determines the graph of basic activities, which identifies the set of activities (i.e., class-server pairs) that are operational. In this paper we explore the extended HTC, where the LP is merely assumed to be critical. Because multiple so...
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作者：Kramkov, Dmitry; Sirbu, Mihai
作者单位：Carnegie Mellon University; University of Texas System; University of Texas Austin
摘要：We study an optimal transport problem with a backward martingale constraint in a pseudo-Euclidean space S. We show that the dual problem consists in the minimization of the expected values of the Fitzpatrick functions associated with maximal S-monotone sets. An optimal plan. and an optimal maximal S-monotone set G are characterized by the condition that the support of. is contained in the graph of the S-projection on G. For a Gaussian random variable Y, we get a unique decomposition: Y = X+ Z,...
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作者：Budhiraja, Amarjit; Johnson, Dane
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Elon University
摘要：We consider a family of resource sharing networks, known as bandwidth sharing models, in heavy traffic with general service and interarrival times. These networks, introduced in Massoulie and Roberts (Telecommun. Syst. 15 (2000) 185-201) as models for internet flows, have the feature that a typical job may require simultaneous processing by multiple resources in the network. We construct simple form threshold policies that asymptotically achieve the Hierarchical Greedy Ideal (HGI) performance....
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作者：Hutchcroft, Tom
作者单位：California Institute of Technology
摘要：We prove up-to-constants bounds on the two-point function (i.e., point-to-point connection probabilities) for critical long-range percolation on the d-dimensional hierarchical lattice. More precisely, we prove that if we connect each pair of points x and y by an edge with probability 1 - exp(- beta parallel to x - y parallel to(-d-alpha)), where 0< alpha < d is fixed and beta >= 0 is a parameter, then the critical two-point function satisfies P-beta c (x <-> y) (sic) parallel to x - y parallel...
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作者：Kuntz, Juan; Crucinio, Francesca R.; Johansen, Adam M.
作者单位：University of Warwick; Institut Polytechnique de Paris; ENSAE Paris
摘要：We provide a comprehensive characterisation of the theoretical properties of the divide-and-conquer sequential Monte Carlo (DaC-SMC) algorithm. We firmly establish it as a well-founded method by showing that it possesses the same basic properties as conventional sequential Monte Carlo (SMC) algorithms do. In particular, we derive pertinent laws of large numbers, Lp inequalities, and central limit theorems; and we characterize the bias in the normalized estimates produced by the algorithm and a...
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作者：Manole, Tudor; Niles-Weed, Jonathan
作者单位：Carnegie Mellon University; New York University
摘要：We revisit the question of characterizing the convergence rate of plug-in estimators of optimal transport costs. It is well known that an empirical measure comprising independent samples from an absolutely continuous distribution on R-d converges to that distribution at the rate n(-1/d) in Wasserstein distance, which can be used to prove that plug-in estimators of many optimal transport costs converge at this same rate. However, we show that when the cost is smooth, this analysis is loose: plu...
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作者：Bayraktar, Erhan; Guo, Gaoyue; Tang, Wenpin; Zhang, Yuming Paul
作者单位：University of Michigan System; University of Michigan; Universite Paris Saclay; Universite Paris Saclay; Columbia University; University of California System; University of California San Diego
摘要：This paper is concerned with the analysis of blow-ups for two McKean-Vlasov equations involving hitting times. Let (B(t); t >= 0) be standard Brownian motion, and tau := inf{t >= 0 : X(t) <= 0} be the hitting time to zero of a given process X. The first equation is X(t) = X(0-) + B(t) - alpha P(tau <= t). We provide a simple condition on a and the distribution of X(0-) such that the corresponding Fokker-Planck equation has no blow-up, and thus the McKean-Vlasov dynamics is well defined for all...
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作者：Mathews, Joseph; Schmidler, Scott C.
作者单位：Duke University
摘要：We prove finite sample complexities for sequential Monte Carlo (SMC) algorithms which require only local mixing times of the associated Markov kernels. Our bounds are particularly useful when the target distribution is multimodal and global mixing of the Markov kernel is slow; in such cases our approach establishes the benefits of SMC over the corresponding Markov chain Monte Carlo (MCMC) estimator. The lack of global mixing is addressed by sequentially controlling the bias introduced by SMC r...
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作者：Erdos, Laszlo; McKenna, Benjamin
作者单位：Institute of Science & Technology - Austria
摘要：We consider quadratic forms of deterministic matrices A evaluated at the random eigenvectors of a large N x N GOE or GUE matrix, or equivalently evaluated at the columns of a Haar-orthogonal or Haar-unitary random matrix. We prove that, as long as the deterministic matrix has rank much smaller than root N, the distributions of the extrema of these quadratic forms are asymptotically the same as if the eigenvectors were independent Gaussians. This reduces the problem to Gaussian computations, wh...
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作者：Qin, Qian; Wang, Guanyang
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Rutgers University System; Rutgers University New Brunswick
摘要：Random-scan Gibbs samplers possess a natural hierarchical structure. The structure connects Gibbs samplers targeting higher-dimensional distributions to those targeting lower-dimensional ones. This leads to a quasi-telescoping property of their spectral gaps. Based on this property, we derive three new bounds on the spectral gaps and convergence rates of Gibbs samplers on general domains. The three bounds relate a chain's spectral gap to, respectively, the correlation structure of the target d...
