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作者：Hwang, HK
作者单位：Academia Sinica - Taiwan
摘要：We study the convergence rate to normal limit law for the space requirement of random m-ary search trees. While it is known that the random variable is asymptotically normally distributed for 3 less than or equal to m less than or equal to 26 and that the limit law does not exist for m > 26, we show that the convergence rate is O(n(-1/2)) for 3 less than or equal to m less than or equal to 19 and is O(n(-3(3/2-alpha))), where 4/3 < alpha < 3/2 is a parameter depending on m for 20 less than or ...
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作者：Mattner, L
作者单位：University of Lubeck
摘要：This is a contribution to the theory of sums of independent random variables at the level of optimal explicit inequalities: we compute the optimal constants in Hornich's lower bounds for the mean absolute deviations of sample means. This is done by reducing the original problem to the elementary one of determining the minimally concentrated binomial distributions B-n,B-p with fixed sample size parameter n.
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作者：Chen, X; Li, WBV
作者单位：University of Tennessee System; University of Tennessee Knoxville; University of Delaware
摘要：Let the Gaussian process X-m(t) be the m-fold integrated Brownian motion for positive integer m. The Laplace transform of the quadratic functional of Xm(t) is found by using an appropriate self-adjoint integral operator. The result is then used to show the power of a general connection between small ball probabilities for the Gaussian process. The connection is discovered by introducing an independent random shift. The interplay between our results and the principal eigenvalues for nonuniform ...
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作者：Harrelson, D; Houdré, C
作者单位：Hope College; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University System of Georgia; Georgia Institute of Technology
摘要：m-dependent stationary infinitely divisible sequences are characterized as a class of generalized finite moving average sequences via the structure of the associated Levy measure. This characterization is used to find necessary and sufficient conditions for the weak convergence of centered and normalized partial sums of m-dependent stationary infinitely divisible sequences. Partial sum convergence for stationary infinitely divisible sequences that can be approximated by m-dependent ones is the...
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作者：Steele, JM; Zhang, Y
作者单位：University of Pennsylvania; University of Colorado System; University of Colorado at Colorado Springs
摘要：We study the paths of minimal cost for first-passage percolation in two dimensions and obtain an exponential bound on the tail probability of the ratio of the lengths of the shortest and longest of these. This inequality permits us to answer a long-standing question of Hammersley and Welsh on the shift differentiability of the time constant. Specifically, we show that for subcritical Bernoulli percolation the time constant is not shift differentiable when p is close to one-half.
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作者：Taylor, JE; Adler, RJ
作者单位：Stanford University; Technion Israel Institute of Technology
摘要：We are interested in the geometric properties of real-valued Gaussian random fields defined on manifolds. Our manifolds, M, are of class C-3 and the random fields f are smooth. Our interest in these fields focuses on their excursion sets, f(-1)[u, + infinity), and their geometric properties. Specifically, we derive the expected Euler characteristic E[chi(f(-1)[u, + infinity))] of an excursion set of a smooth Gaussian random field. Part of the motivation for this comes from the fact that E[chi(...
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作者：Duquesne, T
作者单位：Universite Paris Saclay
摘要：In this work, we study asymptotics of the genealogy of Galton-Watson processes conditioned on the total progeny. We consider a fixed, aperiodic and critical offspring distribution such that the rescaled Galton-Watson processes converges to a continuous-state branching process (CSBP) with a stable. branching mechanism of index a e (1, 2]. We code the genealogy by two different processes: the contour process and the height process that Le Gall and Le Jan recently introduced [21, 22]. We show tha...
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作者：De La Peña, VH; Ibragimov, R; Sharakhmetov, S
作者单位：Columbia University; Yale University; Tashkent State University of Economics
摘要：In this paper we present a study of the problem of approximating the expectations of functions of statistics in independent and dependent random variables in terms of the expectations of functions of the component random variables. We present results providing sharp analogues of the Burkholder-Rosenthal inequalities and related estimates for the expectations of functions of sums of dependent nonnegative r.v.'s and conditionally symmetric martingale differences with bounded conditional moments ...
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作者：Fahrner, I; Stadtmüller, U
作者单位：Ulm University
摘要：Extending results by P. Deheuvels of 1981-1983 we give strong approximation results for sample maxima by simple transformations of extremal processes and discuss the quality of the approximations. The limiting process becomes stationary after a transformation of the argument.
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作者：Talagrand, M
作者单位：Sorbonne Universite
摘要：Physicists have studied the stochastic assignment problem using ideas from statistical mechanics. For a version of this problem, we give, at high enough temperature, a complete proof of the existence of the structure they predict.
