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作者：Vitale, RA
摘要：The Wills functional from the theory of lattice point enumeration can be adapted to produce the following exponential inequality for zero-mean Gaussian processes: E exp[sup(t)(X(t) - (1/2)sigma(t)(2))] less than or equal to exp(E sup(t)X(t)). An application is a new proof of the deviation inequality for the supremum of a Gaussian process above its mean: P(sup(t)X(t) - E sup(t)X(t) greater than or equal to a) less than or equal to exp(-(1/2)alpha(2)/sigma(2)), where alpha > 0 and sigma(2) = sup...
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作者：Cvitanic, J; Karatzas, I
作者单位：Columbia University
摘要：We establish existence and uniqueness results for adapted solutions of backward stochastic differential equations (BSDE's) with two reflecting barriers, generalizing the work of El Karoui, Kapoudjian, Pardoux, Peng and Quenez. Existence is proved first by solving a related pair of coupled optimal stopping problems, and then, under different conditions, via a penalization method. It is also shown that the solution coincides with the value of a certain Dynkin game, a stochastic game of optimal s...
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作者：Gravner, J; Griffeath, D
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：In the threshold growth model on an integer lattice, the occupied set grows according to a simple local rule: a site becomes occupied iff it sees at least a threshold number of already occupied sites in its prescribed neighborhood In this paper, we analyze the behavior of two-dimensional threshold growth dynamics started from a sparse Bernoulli density of occupied sites. We explain how nucleation of rare centers, invariant shapes and interaction between growing droplets influence the first pas...
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作者：Fukai, Y; Uchiyama, K
摘要：It is proved that the potential kernel of a recurrent, aperiodic random walk on the integer lattice Z(2) admits an asymptotic expansion of the form (2 pi root\Q\)(-1)ln Q(x(2), - x(1)) + const + \x\U--1(1)(omega(x)) + \x\U--2(2)(omega(2)) + ..., where \Q\ and Q(theta) are, respectively, the determinant and the quadratic form of the covariance matrix of the increment X of the random walk, omega(2) = x/\x\ and the U-h(omega) are smooth functions of omega, \omega\ = 1, provided that all the momen...
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作者：Alexander, KS
摘要：Every two-dimensional incompressible flow follows the level lines of some scalar function psi on R(2); transport properties of the flow depend in part on whether all level lines are bounded. We study the structure of the level lines when psi is a stationary random held. We show that under mild hypotheses there is only one possible alternative to bounded level lines: the ''treelike'' random fields, which, for some interval of values of a, have a unique unbounded level line at each level a, with...
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作者：Landim, C; Sethuraman, S; Varadhan, S
作者单位：New York University
摘要：We give a lower bound on the spectral gap for symmetric zero-range processes. Under same conditions on the rate function, we show that the gap shrinks as n(-2) independent of the density, for the dynamics localized on a cube of size n(d). We follow the method outlined by Lu and Yau, where a similar spectral gap is proved for Kawasaki dynamics.
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作者：Stacey, AM
摘要：Let T-d be a homogeneous tree in which every vertex has d neighbors. A new proof is given that the contact process on T-d exhibits two phase transitions when d greater than or equal to 3, a behavior which distinguishes it from the contact process on Z(n). This is the first proof which does not involve calculation of bounds on critical values, and it is much shorter than the previous proof for the binary tree, T-3. The method is extended to prove the existence of an intermediate phase for a mor...
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作者：Bramson, M; Cox, JT; Durrett, R
作者单位：Syracuse University; Cornell University
摘要：The relationship between species number and area is an old problem in biology. We propose here an interacting particle system-the multitype Voter model with mutation-as a mathematical model to study this problem. We analyze the species area curves of this model as the mutation rate alpha tends to zero. We obtain two basic types of behavior depending on the size of the spatial region under consideration. If the region is a square with area alpha(-r), r > 1, then, for small alpha, the number of ...
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作者：Evans, SN; Fleischmann, K
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：A stepping-stone model with site space a continuous, hierarchical group is constructed via duality with a system of (delayed) coalescing ''stable'' Levy processes, This model can be understood as a continuum Limit of discrete state-space, two-allele, genetics models with hierarchically structured resampling and migration. The existence of a process rescaling limit on suitably related large space and time scales is established and interpreted in terms of the dynamics of cluster formation. This ...
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作者：Penrose, MD
摘要：For the minimal spanning tree on n independent uniform points in the d-dimensional unit cube, the proportionate number of points of degree k is known to converge to a limit alpha(k,d) as n --> infinity. We show that alpha(k,d) converges to a limit alpha(k) as d --> infinity for each k. The limit alpha(k) arose in earlier work by Aldous, as the asymptotic proportionate number of vertices of degree k in the minimum-weight spanning tree on k vertices, when the edge weights are taken to be indepen...
