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作者：Chaumont, Loic; Kyprianou, Andreas; Carlos Pardo, Juan; Rivero, Victor
作者单位：Universite d'Angers; University of Bath; CIMAT - Centro de Investigacion en Matematicas
摘要：For a positive self-similar Markov process, X, we construct a local time for the random set, Theta, of times where the process reaches its past supremum. Using this local time we describe an exit system for the excursions of X out of its past supremum. Next, we define and study the ladder process (R, H) associated to a positive self-similar Markov process X, namely a bivariate Markov process with a scaling property whose coordinates are the right inverse of the local time of the random set The...
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作者：Jin, Xiong
作者单位：Universite Paris 13; Centre National de la Recherche Scientifique (CNRS)
摘要：We prove a Hausdorff dimension result for the image of two-dimensional multiplicative cascade processes, and we obtain from this result a KPZ-type formula which normally has one point of phase transition.
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作者：Aaronson, Jon
作者单位：Tel Aviv University
摘要：Relative complexity measures the complexity of a probability preserving transformation relative to a factor being a sequence of random variables whose exponential growth rate is the relative entropy of the extension. We prove distributional limit theorems for the relative complexity of certain zero entropy extensions: RWRSs whose associated random walks satisfy the alpha-stable CLT (1 < alpha <= 2). The results give invariants for relative isomorphism of these.
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作者：Dalang, Robert C.; Khoshnevisan, Davar; Nualart, Eulalia; Wu, Dongsheng; Xiao, Yimin
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Utah System of Higher Education; University of Utah; Universite Paris 13; University of Alabama System; University of Alabama Huntsville; Michigan State University
摘要：We derive a decoupling formula for the Brownian sheet which has the following ready consequence: An N-parameter Brownian sheet in R-d has double points if and only if d < 4N. In particular, in the critical case where d = 4N, the Brownian sheet does not have double points. This answers an old problem in the folklore of the subject. We also discuss some of the geometric consequences of the mentioned decoupling, and establish a partial result concerning k-multiple points in the critical case k(d ...
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作者：Dette, Holger; Nagel, Jan
作者单位：Ruhr University Bochum; Technical University of Munich
摘要：In this paper we define distributions on moment spaces corresponding to measures on the real line with an unbounded support. We identify these distributions as limiting distributions of random moment vectors defined on compact moment spaces and as distributions corresponding to random spectral measures associated with the Jacobi, Laguerre and Hermite ensemble from random matrix theory. For random vectors on the unbounded moment spaces we prove a central limit theorem where the centering vector...
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作者：Ledoux, M.
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Institut Universitaire de France
摘要：We analyze from the viewpoint of an abstract Markov operator recent results by Nualart and Peccati, and Nourdin and Peccati, on the fourth moment as a condition on a Wiener chaos to have a distribution close to Gaussian. In particular, we are led to introduce a notion of chaos associated to a Markov operator through its iterated gradients and present conditions on the (pure) point spectrum for a sequence of chaos eigenfunctions to converge to a Gaussian distribution. Convergence to gamma distr...
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作者：Kemp, Todd; Nourdin, Ivan; Peccati, Giovanni; Speicher, Roland
作者单位：University of California System; University of California San Diego; Universite de Lorraine; University of Luxembourg; Saarland University
摘要：We prove that a normalized sequence of multiple Wigner integrals (in a fixed order of free Wigner chaos) converges in law to the standard semicircular distribution if and only if the corresponding sequence of fourth moments converges to 2, the fourth moment of the semicircular law. This extends to the free probabilistic, setting some recent results by Nualart and Peccati on characterizations of central limit theorems in a fixed order of Gaussian Wiener chaos. Our proof is combinatorial, analyz...
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作者：Chen, Zhen-Qing; Kim, Panki; Song, Renming
作者单位：University of Washington; University of Washington Seattle; Seoul National University (SNU); University of Illinois System; University of Illinois Urbana-Champaign
摘要：In this paper, we establish sharp two-sided estimates for the transition densities of relativistic stable processes [i.e., for the heat kernels of the operators m - (m(2/alpha) - Delta)(alpha/2)] in C-1,C-1 open sets. Here m > 0 and alpha is an element of (0, 2). The estimates are uniform in m is an element of (0, M] for each fixed M > 0. Letting m down arrow 0, we recover the Dirichlet heat kernel estimates for Delta(alpha/2) := -(-Delta)(alpha/2) in C-1,C-1 open sets obtained in [14]. Sharp ...
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作者：Pittel, Boris
作者单位：University System of Ohio; Ohio State University
摘要：For an ergodic Markov chain {X (t)} on N, with a stationary distribution pi, let T-n > 0 denote a hitting time for [n](c), and let X-n = X (T-n). Around 2005 Guy Louchard popularized a conjecture that, for n -> infinity, T-n is almost Geometric(p), p = pi([n](c)), X-n is almost stationarily distributed on [n](c) and that X-n and T-n are almost independent, if p(n) := sup(i) p(i,[n](c)) -> 0 exponentially fast. For the chains with p(n) -> 0, however slowly, and with sup(i,j) parallel to p(i, .)...
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作者：Keller, Nathan; Mossel, Elchanan; Sen, Arnab
作者单位：Weizmann Institute of Science; University of California System; University of California Berkeley; University of Cambridge
摘要：We present a new definition of influences in product spaces of continuous distributions. Our definition is geometric, and for monotone sets it is identical with the measure of the boundary with respect to uniform enlargement. We prove analogs of the Kahn-Kalai-Linial (KKL) and Talagrand's influence sum bounds for the new definition. We further prove an analog of a result of Friedgut showing that sets with small influence sum are essentially determined by a small number of coordinates. In parti...
