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作者：Bressaud, Xavier; Fournier, Nicolas
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel
摘要：We consider the so-called one-dimensional forest fire process. At each site of Z, a tree appears at rate 1. At each site of Z, a fire starts at rate lambda > 0, immediately destroying the whole corresponding connected component of trees. We show that when lambda is made to tend to 0 with an appropriate normalization, the forest tire process tends to a uniquely defined process, the dynamics of which we precisely describe. The normalization consists of accelerating time by a factor log(1/lambda)...
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作者：Burdzy, Krzysztof; Swanson, Jason
作者单位：University of Washington; University of Washington Seattle; State University System of Florida; University of Central Florida
摘要：We consider the solution u(x, t) to a stochastic heat equation. For fixed x, the process F(t) = u(x, t) has a nontrivial quartic variation. It follows that F is not a semimartingale, so a stochastic integral with respect to F cannot be defined in the classical Ito sense. We show that for sufficiently differentiable functions g(x, t), a stochastic integral integral g(F(t), t)d F(t) exists as a limit of discrete, midpoint-style Riemann sums, where the limit is taken in distribution in the Skorok...
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作者：Peligrad, Magda; Wu, Wei Biao
作者单位：University System of Ohio; University of Cincinnati; University of Chicago
摘要：We consider asymptotic behavior of Fourier transforms of stationary ergodic sequences with finite second moments. We establish a central limit theorem (CLT) for almost all frequencies and also an annealed CLT. The theorems hold for all regular sequences. Our results shed new light on the foundation of spectral analysis and on the asymptotic distribution of periodogram, and it provides a nice blend of harmonic analysis, theory of stationary processes and theory of martingales.
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作者：Tao, Terence; Vu, Van; Krishnapur, Manjunath
作者单位：University of California System; University of California Los Angeles; Rutgers University System; Rutgers University New Brunswick; Indian Institute of Science (IISC) - Bangalore
摘要：Given an n x n complex matrix A, let mu(A)(x, y) := 1/n vertical bar{1 <= i <= n, Re lambda(i) <= x, Im lambda(i) <= y}vertical bar be the empirical spectral distribution (ESD) of its eigenvalues lambda(i) is an element of C, i = l, ... , n. We consider the limiting distribution (both in probability and in the almost sure convergence sense) of the normalized ESD mu(1/root n An) of a random matrix A(n) = (a(ij))(1 <= i, j <= n), where the random variables a(ij) - E(a(ij)) are i.i.d. copies of a...
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作者：Fribergh, Alexander
作者单位：New York University
摘要：We study the speed of a biased random walk on a percolation cluster on Z(d) in function of the percolation parameter p. We obtain a first order expansion of the speed at p = 1 which proves that percolating slows down the random walk at least in the case where the drift is along a component of the lattice.
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作者：Bogdan, Krzysztof; Grzywny, Tomasz; Ryznar, Michal
作者单位：Wroclaw University of Science & Technology
摘要：We give sharp estimates for the heat kernel of the fractional Laplacian with Dirichlet condition for a general class of domains including Lipschitz domains.
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作者：Astashkin, S. V.; Sukochev, F. A.
作者单位：Samara National Research University; University of New South Wales Sydney
摘要：Let X be a symmetric Banach function space on [0, 1] with the Kruglov property, and let f = {f(k)}(k=1)(n), n > 1 be an arbitrary sequence of independent random variables in X. This paper presents sharp estimates in the deterministic characterization of the quantities parallel to Sigma(n)(k=1) f(k)parallel to(X), parallel to(Sigma(n)(k=1)vertical bar f(k)vertical bar(p))(1/p)parallel to(X), 1 <= p < infinity, in terms of the sum of disjoint copies of individual terms of f. Our method is novel ...
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作者：Nourdin, Ivan; Peccati, Giovanni; Reinert, Gesine
作者单位：Universite Paris Cite; Sorbonne Universite; University of Luxembourg; University of Oxford
摘要：We compute explicit bounds in the normal and chi-square approximations of multilinear homogenous sums (of arbitrary order) of general centered independent random variables with unit variance. In particular, we show that chaotic random variables enjoy the following form of universality: (a) the normal and chi-square approximations of any homogenous sum can be completely characterized and assessed by first switching to its Wiener chaos counterpart, and (b) the simple upper bounds and convergence...
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作者：Barral, Julien; Fournier, Nicolas; Jaffard, Stephane; Seuret, Stephane
作者单位：Universite Paris 13; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：We construct a nondecreasing pure jump Markov process, whose jump measure heavily depends on the values taken by the process. We determine the singularity spectrum of this process, which turns out to be random and to depend locally on the values taken by the process. The result relies on fine properties of the distribution of Poisson point processes and on ubiquity theorems.
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作者：Blanchard, Philippe; Roeckner, Michael; Russo, Francesco
作者单位：University of Bielefeld; University of Bielefeld; Purdue University System; Purdue University; Institut Polytechnique de Paris; Ecole des Ponts ParisTech; Institut Polytechnique de Paris; ENSTA Paris
摘要：We consider a porous media type equation over all of R-d, d = 1, with monotone discontinuous coefficient with linear growth, and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion. The interest in such singular porous media equations is due to the fact that they can model systems exhibiting the phenomenon of self-organized criticality. One of the main analytic ingredients of the proof is a new result on uniqueness of distributional solutions of...
