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作者：Chayes, L; Schonmann, RH
作者单位：University of California System; University of California Los Angeles
摘要：By using mixed percolation as a bridge between site and band percolation, me derive a nem inequality between the critical points of these processes that is optimal in a certain sense, We also extend a result on the crossover exponent of bond-diluted Potts models to site-diluted Potts models. Same new results about the critical line in mixed percolation are also proved.
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作者：Evans, W; Kenyon, C; Peres, Y; Schulman, LJ
作者单位：University of Arizona; Universite Paris Saclay; University of California System; University of California Berkeley; Hebrew University of Jerusalem; University System of Georgia; Georgia Institute of Technology
摘要：Consider a process in which information is transmitted from a given root node on a noisy tree network T. We start with an unbiased random bit R at the root of the tree and send it down the edges of T. On every edge the bit can be reversed with probability epsilon, and these errors occur independently. The goal is to reconstruct R from the values which arrive at the nth level of the tree. This model has been studied in information theory, genetics and statistical mechanics. We bound the reconst...
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作者：Coffman, EG; Flatto, L; Jelenkovic, P
作者单位：Alcatel-Lucent; Lucent Technologies; AT&T; Columbia University
摘要：Starting at time 0, unit-length intervals arrive and are placed on the positive real line by a unit-intensity Poisson process in two dimensions; the left endpoints of intervals appear at the rate of 1 per unit time per unit distance. An arrival is accepted if and only if, for some given x, the interval is contained in [0, x] and overlaps no interval already accepted. This stochastic, on-line interval packing problem generalizes the classical parking problem, the latter corresponding only to th...
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作者：Huebner, M; Lototsky, S
作者单位：Michigan State University; Massachusetts Institute of Technology (MIT)
摘要：In this paper we construct a kernel estimator of a time-varying coefficient of a strongly elliptic partial differential operator in a stochastic parabolic equation. The equation is assumed diagonalizable; that is, all the operators have a common system of eigenfunctions. The mean-square convergence of the estimator is established. The rate of convergence is determined both by the smoothness of the true coefficient and by the asymptotics of the eigenvalues of the operators in the equation.
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作者：Chen, H; Shen, XY
作者单位：University of British Columbia
摘要：This paper derives the strong approximation for a muiticlass queueing network, where jobs after service completion can only move to a downstream service station. Job classes are partitioned into groups. Within a group, jobs are served in the order of arrival; that is, a first-in first-out (FIFO) discipline is in force, and among groups, jobs are served under a preassigned preemptive priority discipline. We obtain the strong approximation for the network through an inductive application of an i...
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作者：Arratia, R; Barbour, AD; Tavaré, S
作者单位：University of Southern California; University of Zurich
摘要：Under very mild conditions, we prove that the number of components in a decomposable logarithmic combinatorial structure has a distribution which is close to Poisson in total variation. The conditions are satisfied for all assemblies, multisets and selections in the logarithmic class. The error in the Poisson approximation is shown under marginally more restrictive conditions to be of exact order O(1/ log n), by exhibiting the penultimate asymptotic approximation; similar results have previous...
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作者：Penrose, MD
作者单位：Durham University
摘要：Given an ordering of the vertices of a finite graph, let the induced weight for an edge be the separation of its endpoints in the ordering. Layout problems involve choosing the ordering to minimize a cost functional such as the sum or maximum of the edge weights. We give growth rates for the costs of some of these problems on supercritical percolation processes and supercritical random geometric graphs, obtained by placing vertices randomly in the unit cube and joining them whenever at most so...
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作者：Yin, G; Zhang, Q; Badowski, G
作者单位：Wayne State University; University System of Georgia; University of Georgia
摘要：This work is concerned with aggregations in a singularly perturbed Markov chain having a finite state space and fast and slow motions. The state space of the underlying Markov chain can be decomposed into several groups of recurrent states and a group of transient states. The asymptotic properties are studied through sequences of unscaled and scaled occupation measures. By treating the states within each recurrent class as a single state, an aggregated process is defined and shown to be conver...
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作者：Bouchard, B; Touzi, N
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：We consider a multivariate financial market with transaction costs as in Kabanov. We study the problem of finding the minimal initial capital needed to hedge, without risk, European-type contingent claims. We prove that the value of this stochastic control problem is given by the cost of the cheapest buy-and-hold strategy. This is an extension of the already known result in the one-dimensional case. An important feature of our analysis is that we do not make use of the dual formulation of the ...
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作者：Giraitis, L; Robinson, PM; Surgailis, D
作者单位：University of London; London School Economics & Political Science; Vilnius University
摘要：For a particular conditionally heteroscedastic nonlinear (ARCH) process for which the conditional variance of the observable sequence r(t) is the square of an inhomogeneous linear combination of r(s), s < t, we give conditions under which, for integers l 2, r(t)(l) has long memory autocorrelation and normalized partial sums of r(t)(l) converge to fractional Brownian motion.
