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作者：Amini, Omid; Devroye, Luc; Griffiths, Simon; Olver, Neil
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); McGill University; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Massachusetts Institute of Technology (MIT)
摘要：Consider a branching random walk on R, with offspring distribution Z and nonnegative displacement distribution W. We say that explosion occurs if an infinite number of particles may be found within a finite distance of the origin. In this paper, we investigate this phenomenon when the offspring distribution Z is heavy-tailed. Under an appropriate condition, we are able to characterize the pairs (Z, W) for which explosion occurs, by demonstrating the equivalence of explosion with a seemingly mu...
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作者：Anderson, Greg W.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：For polynomials in independent Wigner matrices, we prove convergence of the largest singular value to the operator norm of the corresponding polynomial in free semicircular variables, under fourth moment hypotheses. We actually prove a more general result of the form no eigenvalues outside the support of the limiting eigenvalue distribution. We build on ideas of Haagerup-Schultz-Thorbjornsen on the one hand and Bai-Silverstein on the other. We refine the linearization trick so as to preserve s...
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作者：Schreiber, Tomasz; Thaele, Christoph
作者单位：Nicolaus Copernicus University; University Osnabruck
摘要：The intent of this paper is to describe the large scale asymptotic geometry of iteration stable (STIT) tessellations in R-d, which form a rather new, rich and flexible class of random tessellations considered in stochastic geometry. For this purpose, martingale tools are combined with second-order formulas proved earlier to establish limit theorems for STIT tessellations. More precisely, a Gaussian functional central limit theorem for the surface increment process induced a by STIT tessellatio...
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作者：Cheliotis, Dimitris; den Hollander, Frank
作者单位：National & Kapodistrian University of Athens; Leiden University - Excl LUMC; Leiden University
摘要：In this paper we look at the pinning of a directed polymer by a one-dimensional linear interface carrying random charges.. There are two phases, localized and delocaliied, depending on the inverse temperature and on the disorder bias. Using quenched and annealed large deviation principles for the empirical process of words drawn from a random letter sequence according to a random renewal process [Birkner, Greven and den Hollander, Probab. Theory Related Fields 148 (2010) 403-456], we derive va...
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作者：Friedli, S.; Ioffe, D.; Velenik, Y.
作者单位：Universidade Federal de Minas Gerais; Technion Israel Institute of Technology; University of Geneva
摘要：We consider the Bernoulli bond percolation process P-p,P-p' on the nearestneighbor edges of Z(d), which are open independently with probability p < p(c), except for those lying on the first coordinate axis, for which this probability is p'. Define xi(p,p') := - lim(n ->infinity) n(-1) log P-p,P-p' (0 <-> -ne(1)) and xi(p) := xi(p,p). We show that there exists p(c)' = p(c)'(p, d) such that xi(p,p)' = xi(p) if p' < p(c)' and xi(p,p)' < xi(p) if p' > p(c)'. Moreover, p(c)'(p, 2) = p(c)'(p, 3) = p...
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作者：Conus, Daniel; Joseph, Mathew; Khoshnevisan, Davar
作者单位：Lehigh University; Utah System of Higher Education; University of Utah
摘要：We consider a nonlinear stochastic heat equation at partial derivative(t)u = 1/2 partial derivative(xx)u + sigma(u)partial derivative W-xt, where partial derivative(xt) W denotes space time white noise and sigma : R -> R is Lipschitz continuous. We establish that, at every fixed time t > 0, the global behavior of the solution depends in a critical manner on the structure of the initial function u(0): under suitable conditions on u(0) and sigma, sup(x is an element of R)u(t)(x) is a.s. finite w...
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作者：Barrieu, Pauline; El Karoui, Nicole
作者单位：University of London; London School Economics & Political Science; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
摘要：In this paper, we study the stability and convergence of some general quadratic semimartingales. Motivated by financial applications, we study simultaneously the semimartingale and its opposite. Their characterization and integrability properties are obtained through some useful exponential sub-martingale inequalities. Then, a general stability result, including the strong convergence of the martingale parts in various spaces ranging from H-1 to BMO, is derived under some mild integrability co...
