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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...
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作者：Bhati, AG; Borkar, VS
作者单位：Indian Institute of Science (IISC) - Bangalore
摘要：For controlled Markov processes taking values in a Polish space, control problems with ergodic cost, infinite-horizon discounted cost and finite-horizon cost are studied. Each is posed as a convex optimization problem wherein one tries to minimize a linear functional on a closed convex set of appropriately defined occupation measures for the problem. These are characterized as solutions of a linear equation asssociated with the problem. This characterization is used to establish the existence ...
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作者：Bunge, J
摘要：A random variable X is N-divisible if it can be decomposed into a random sum of N i.i.d. components, where N is a random variable independent of the components; X is N-stable if the components are rescaled copies of X. These N-divisible and N-stable random variables arise in a variety of stochastic models, including thinned renewal processes and subordinated Levy and stable processes. We consider a general theory of N-divisibility and N-stability in the case where E(N) < infinity, based on a r...
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作者：Donnelly, P; Kurtz, TG
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：The Fleming-Viot measure-valued diffusion arises as the infinite population limit of various discrete genetic models with general type space. The paper gives a countable construction of the process as the empirical measure carried by a certain interactive particle system. This explicit representation facilitates the study of various properties of the Fleming-Viot process. The construction also carries versions of the familiar genealogical processes from population genetics, in particular, King...
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作者：Roichman, Y
摘要：We estimate the expected mixing time of a random walk on a finite group supported by a random polylogarithmic set of elements. Following the spectral approach of Broder and Shamir, we present an alternative proof of the Dou-Hildebrand estimate and show that it holds almost surely. Good bounds on diameters follow from these results.
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作者：Porod, U
摘要：For many random walks on ''sufficiently large'' finite groups the so-called cut-off phenomenon occurs: roughly stated, there exists a number k(0), depending on the size of the group, such that it, steps are necessary and sufficient for the random walk to closely approximate uniformity. As a first example on a continuous group, Rosenthal recently proved the occurrence of this cut-off phenomenon for a specific random walk on SO(N). Here we present and [for the case of O(N)] prove results for ran...
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作者：Bertoin, J; Werner, W
作者单位：Centre National de la Recherche Scientifique (CNRS); University of Cambridge
摘要：We derive the asymptotic laws of winding numbers for planar isotropic stable Levy processes and walks of index alpha is an element of (0, 2).
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作者：Kersting, G
摘要：For a class of diffusions X in the plane we construct a global system of coordinates u(x), such that u(x) is close to x at infinity and u(X) is a local martingale. Such coordinates are useful for the study of the long term behaviour of X. The construction uses probabilistic methods, in particular a coupling for general diffusions in the plane.
