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作者：Landim, Claudio; Misturini, Ricardo; Sau, Federico
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidade Federal do Rio Grande do Sul; University of Trieste
摘要：Let E-n subset of R-d, n >= 1, be a sequence of finite sets and consider a E-n-valued, irreducible, reversible, continuous-time Markov chain (X-t((n)):t >= 0). Denote by P(R-d) the set of probability measures on R-d and by I-n:P(R-d)->[0,+infinity) the level two large deviations rate functional for X(t )((n))as t ->infinity. We present a general method, based on tools used to prove the metastable behaviour of Markov chains, to derive a full expansion of InIn expressing it as I-n=I-(0)+& sum;(1...
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作者：Biskup, Marek; Krieger, Andrew
作者单位：University of California System; University of California Los Angeles
摘要：We consider a long-range percolation graph on Z(d) where, in addition to the nearest-neighbor edges of Z(d) , distinct x,y is an element of Z(d) are connected by an edge independently with probability asymptotic to beta|x - y|(-s), for s is an element of (d, 2 d) , beta > 0 and |center dot| a norm on R-d. We first show that, for all but perhaps a countably many beta > 0, the graph-theoretical (a.k.a. chemical) distance between typical vertices at |center dot|-distance r is, with high probabili...
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作者：Kifer, Yuri
作者单位：Hebrew University of Jerusalem
摘要：It is known since (Theory Probab. Appl. 11 (1966) 390-406) that the slow motion X-epsilon in the time-scaled multidimensional averaging setup dX(epsilon)(t)/dt = 1/epsilon B(X-epsilon(t), xi(t/epsilon(2))) +b(X-epsilon(t), xi(t/epsilon(2))), t is an element of [0, T] converges weakly as epsilon -> 0 to a diffusion process provided EB(x, xi(s)) 0 where xi is a sufficiently fast mixing stochastic process. In this paper we show that both X-epsilon and a family of diffusions Xi(epsilon) can be red...
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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：Lacoin, Hubert; Yang, Shangjie
作者单位：Bar Ilan University
摘要：We consider the simple exclusion process in the integer segment [[1, N]] with k <= N/2 particles and spatially inhomogenous jumping rates. A particle at site x is an element of [[1, Nil jumps to site x - 1 (if x >= 2) at rate 1 - omega(x) and to site x + 1 (if x <= N 1) at rate omega(x) if the target site is not occupied. The sequence omega = (omega(x))(x is an element of Z) is chosen by IID sampling from a probability law whose support is bounded away from zero and one (in other words the ran...
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作者：Bernstein, Daniel Irving; Dewar, Sean; Gortler, Steven J.; Nixon, Anthony; Sitharam, Meera; Theran, L. ouis
作者单位：Tulane University; University of Bristol; Harvard University; Lancaster University; State University System of Florida; University of Florida; University of St Andrews
摘要：The maximum likelihood threshold (MLT) of a graph G is the minimum number of samples to almost surely guarantee existence of the maximum likelihood estimate in the corresponding Gaussian graphical model. We give a new characterization of the MLT in terms of rigidity-theoretic properties of G and use this characterization to give new combinatorial lower bounds on the MLT of any graph. We use the new lower bounds to give high-probability guarantees on the maximum likelihood thresholds of sparse ...
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作者：Chakrabarty, A. rijit; Samorodnitsky, Gennady
作者单位：Indian Statistical Institute; Cornell University
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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...
