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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...
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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：Flammant, Lucas
作者单位：Universite Polytechnique Hauts-de-France; Centre National de la Recherche Scientifique (CNRS)
摘要：The Euclidean directed spanning forest is a random forest in Rd introduced by Baccelli and Bordenave in 2007 and we introduce and study here the analogous tree in the hyperbolic space. The topological properties of the Euclidean DSF have been stated for d = 2 and conjectured for d = 3 (see further): it should be a tree for d is an element of{2, 3} and a countable union of disjoint trees for d >= 4. Moreover, it should not contain bi-infinite branches whatever the dimension d. In this paper, we...
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作者：Li, Liping; Sun, Wenjie
作者单位：Fudan University; Tongji University
摘要：In this paper we study a stiff problem in two-dimensional space and especially characterize its probabilistic counterpart. More specifically, consider the heat equation with a parameter epsilon > 0: partial derivative(t)u(epsilon)(t,x) = 1/2 del (A(epsilon) (x)del u(epsilon)(t,x)), t >= 0 , x is an element of R-2, where A(epsilon) (x) := Id(2), the identity matrix, for x is not an element of Omega(epsilon) := { x = (x(1),x(2)) is an element of R-2: |x(2) | < epsilon } and A(epsilon) (x) := (a(...
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作者：Zheng, Xinghua; Zhu, Qingsan
作者单位：Hong Kong University of Science & Technology; Hong Kong University of Science & Technology
摘要：We study supercritical spatial SIR epidemics on Z2 2 x { 1 , 2 ,.. .,N } , where each site in Z2 2 represents a village and N stands for the village size. We establish several asymptotic results as N-* oc . In particular, we derive the probability that the epidemic will last forever if the epidemic is started by one infected individual.E Moreover, we show that, conditional on that the epidemic lasts forever, the epidemic spreads out linearly in all directions and derive an explicit formula for...
