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作者：Luczak, Malwina J.; McDiarmid, Colin
作者单位：University of London; London School Economics & Political Science; University of Oxford
摘要：There are n queues, each with a single server. Customers arrive in a Poisson process at rate lambda n, where 0 < lambda < 1. Upon arrival each customer selects d >= 2 servers uniformly at random, and joins the queue at a least-loaded server among those chosen. Service times are independent exponentially distributed random variables with mean 1. We show that the system is rapidly mixing, and then investigate the maximum length of a queue in the equilibrium distribution. We prove that with proba...
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作者：Conger, Mark; Viswanath, D.
作者单位：University of Michigan System; University of Michigan
摘要：By a well-known result of Bayer and Diaconis, the maximum entropy model of the common riffle shuffle implies that the number of riffle shuffles necessary to mix a standard deck of 52 cards is either 7 or 11-with the former number applying when the metric used to define mixing is the total variation distance and the latter when it is the separation distance. This and other related results assume all 52 cards in the deck to be distinct and require all 52! permutations of the deck to be almost eq...
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作者：Berestycki, Nathanael
作者单位：University of British Columbia; Universite PSL; Ecole Normale Superieure (ENS)
摘要：Turn the set of permutations of n objects into a graph G, by connecting two permutations that differ by one transposition, and let at be the simple random walk on this graph. In a previous paper, Berestycki and Durrett [In Discrete Random Walks (2005) 17-26] showed that the limiting behavior of the distance from the identity at time cn/2 has a phase transition at c = 1. Here we investigate some consequences of this result for the geometry of G, Our first result can be interpreted as a breakdow...
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作者：Yukich, JE; Zhang, Y
作者单位：Lehigh University; University of Colorado System; University of Colorado at Colorado Springs
摘要：Let 0 < a < b < infinity be fixed scalars. Assign independently to each edge in the lattice Z(2) the value a with probability p or the value b with probability 1 - p. For all u, v is an element of Z(2), let T(u, v) denote the first passage time between u and v. We show that there are points x is an element of R-2 such that the time constant in the direction of x, namely, lim(n ->infinity) n(-1) E-p[T(0, nx)], is not a three times differentiable function of p.
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作者：Hammond, Alan
作者单位：University of California System; University of California Berkeley
摘要：Assign to each site of the integer lattice Z(d) a real score, sampled according to the same distribution F, independently of the choices made at all other sites. A lattice animal is a finite connected set of sites, with its weight being the sum of the scores at its sites. Let N-n be the maximal weight of those lattice animals of size if that contain the origin. Denote by N the almost sure finite constant limit of n(-1) N-n which exists under a mild condition on the positive tail of F. We study...
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作者：Rockner, Michael; Sobol, Zeev
作者单位：Purdue University System; Purdue University; Purdue University System; Purdue University; Swansea University
摘要：We develop a new method to uniquely solve a large class of heat equations. so-called Kolmogorov equations in infinitely many variables. The equations are analyzed in spaces of sequentially weakly continuous functions weighted by proper (Lyapunov type) functions. This way for the first time the solutions are constructed everywhere without exceptional sets for equations with possibly nonlocally Lipschitz drifts. Apart from general analytic interest, the main motivation is to apply this to unique...
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作者：Eisenbaum, Nathalie; Kaspi, Haya
作者单位：Sorbonne Universite; Technion Israel Institute of Technology
摘要：We show that, up to multiplication by constants, a Gaussian process has an infinitely divisible square if and only if its covariance is the Green function of a transient Markov process.
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作者：Broman, Erik I.; Steif, Jeffrey E.
作者单位：Chalmers University of Technology
摘要：In this paper we will investigate dynamic stability of percolation for the stochastic Ising model and the contact process. We also introduce the notion of downward and upward epsilon-movability which will be a key tool for our analysis.
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作者：Kozakova, Iva; Meester, Ronald; Nanda, Seema
作者单位：Vrije Universiteit Amsterdam; Tata Institute of Fundamental Research (TIFR); University of Tennessee System; University of Tennessee Knoxville
摘要：We study the size of connected components of random nearest-neighbor graphs with vertex set the points of a homogeneous Poisson point process in R-d. The connectivity function is shown to decay superexponentially, and we identify the exact exponent. From this we also obtain the decay rate of the maximal number of points of a path through the origin. We define the generation number of a point in a component and establish its asymptotic distribution as the dimension d tends to infinity.
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作者：Lototsky, S. V.; Rozovskii, B. L.
作者单位：University of Southern California
摘要：A new method is described for constructing a generalized solution of a stochastic evolution equation. Existence, uniqueness, regularity and a probabilistic representation of this Wiener Chaos solution are established for a large class of equations. As an application of the general theory, new results are obtained for several types of the passive scalar equation.
