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作者：Dalang, Robert C.; Mueller, C.; Zambotti, L.
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Rochester; Polytechnic University of Milan
摘要：We study the hitting properties of the solutions u of a class of parabolic stochastic partial differential equations with singular drifts that prevent u from becoming negative. The drifts can be a reflecting term or a nonlinearity cu(-3), with c > 0. We prove that almost surely, for all time t > 0, the solution ut hits the level 0 only at a finite number of space points, which depends explicitly on c. In particular, this number of hits never exceeds 4 and if c > 15/8, then level 0 is not hit.
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作者：Sheffield, Scott
作者单位：University of California System; University of California Berkeley
摘要：An essential spanning forest of an infinite graph G is a spanning forest of G in which all trees have infinitely many vertices. Let G(n) be an increasing sequence of finite connected subgraphs of G for which boolean OR G(n) = G. Pemantle's arguments imply that the uniform measures on spanning trees of G, converge weakly to an Aut(G)-invariantmeasure mu(G) on essential spanning forests of G. We show that if G is a connected, amenable graph and F subset of Aut(G) acts quasitransitively on G, the...
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作者：Hoffman, Christopher; Holroyd, Alexander E.; Peres, Yuval
作者单位：University of Washington; University of Washington Seattle; University of British Columbia; University of California System; University of California Berkeley
摘要：Let Xi be a discrete set in R-d. Call the elements of Xi centers. The well-known Voronoi tessellation partitions R-d into polyhedral regions (of varying sizes) by allocating each site of R-d to the closest center. Here we study fair allocations of R-d to Iota in which the regions allocated to different centers have equal volumes. We prove that if Xi is obtained from a translation-invariant point process, then there is a unique fair allocation which is stable in the sense of the Gale-Shapley ma...
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作者：Cohen, G; Cuny, C
作者单位：Ben-Gurion University of the Negev
摘要：We study random exponential sums of the form Sigma(n)(k=1) X-k exp {i (lambda((1))(k) t(1) +(...)+ lambda((s))(k)t(s))}, where {X-n} is a sequence of random variables and {lambda((i))(n) : 1 <= i <= s} are sequences of real numbers. We obtain uniform estimates (on compact sets) of such sums, for independent centered {X-n} or bounded {X-n} satisfying some mixing conditions. These results generalize recent results of Weber [Math. Inequal. Appl. 3 (2000) 443-457] and Fan and Schneider [Ann. Inst....
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作者：Gaertner, J.; den Hollander, F.
作者单位：Technical University of Berlin; Leiden University; Leiden University - Excl LUMC
摘要：In this paper, we study intermittency for the parabolic Anderson equation partial derivative u/partial derivative t = K Delta u + xi u, where u: Z(d) x [0, infinity) -> R, K is the diffusion constant, Delta is the discrete Laplacian and xi : Z(d) X [0, infinity) -> R is a space-time random medium. We focus on the case where xi is gamma times the random medium that is obtained by running independent simple random walks with diffusion constant rho starting from a Poisson random field with intens...
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作者：Gamburd, Alex
作者单位：University of California System; University of California Santa Cruz
摘要：Brooks and Makover introduced an approach to studying the global geometric quantities (in particular, the first eigenvalue of the Laplacian, injectivity radius and diameter) of a typical compact Riemann surface of large genus based on compactifying finite-area Riemann surfaces associated with random cubic graphs; by a theorem of Belyi, these are dense in the space of compact Riemann surfaces. The question as to how these surfaces are distributed in the Teichmuller spaces depends on the study o...
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作者：Evans, Steven N.; Winter, Anita
作者单位：University of California System; University of California Berkeley; University of Erlangen Nuremberg
摘要：We use Dirichlet form methods to construct and analyze a reversible Markov process, the stationary distribution of which is the Brownian continuum random tree. This process is inspired by the subtree prune and regraft (SPR) Markov chains that appear in phylogenetic analysis. A key technical ingredient in this work is the use of a novel Gromov-Hausdorff type distance to metrize the space whose elements are compact real trees equipped with a probability measure. Also, the investigation of the Di...
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作者：Rider, B.; Silverstein, Jack W.
作者单位：University of Colorado System; University of Colorado Boulder; North Carolina State University
摘要：Consider an ensemble of N x N non-Hermitian matrices in which all entries are independent identically distributed complex random variables of mean zero and absolute mean-square one. If the entry distributions also possess bounded densities and finite (4 + epsilon) moments, then Z. D. Bai [Ann. Probab. 25 (1997) 494-529] has shown the ensemble to satisfy the circular law: after scaling by a factor of 1/root N and letting N -> infinity, the empirical measure Of the eigenvalues converges weakly t...
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作者：Chassaing, Philippe; Durhuus, Bergfinnur
作者单位：Universite de Lorraine; University of Copenhagen; University of Copenhagen
摘要：Exploiting a bijective correspondence between planar quadrangulations and well-labeled trees, we define an ensemble of infinite surfaces as a limit of uniformly distributed ensembles of quadrangulations of fixed finite volume. The limit random surface can be described in terms of a birth and death process and a sequence of multitype Galton-Watson trees. As a consequence, we find that the expected volume of the ball of radius r around a marked point in the limit random surface is Theta(r(4)).
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作者：Dembo, A; Peres, Y; Rosen, J; Zeitouni, O
作者单位：Stanford University; Stanford University; City University of New York (CUNY) System; College of Staten Island (CUNY); University of California System; University of California Berkeley; University of California System; University of California Berkeley; Technion Israel Institute of Technology; Technion Israel Institute of Technology; University of Minnesota System; University of Minnesota Twin Cities
摘要：Let T-n(x) denote the time of first visit of a point x on the lattice torus Z(n)(2) = Z(2)/nZ(2) by the simple random walk. The size of the set of alpha, n-late points L-n(alpha) = {x is an element of Z(n)(2): T-n(x) >= alpha(4)/(pi)(n log n)(2)} is approximately n(2(1-alpha)), for alpha is an element of (0, 1) [L-n(alpha) is empty if alpha > 1 and n is large enough]. These sets have interesting clustering and fractal properties: we show that for beta is an element of (0, 1), a disc of radius ...
