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作者：Bryc, Wlodzimierz
作者单位：University System of Ohio; University of Cincinnati
摘要：We derive a non-asymptotic expression for the moments of traces of monomials in several independent complex Wishart matrices, extending some explicit formulas available in the literature. We then deduce the explicit expression for the cumulants. From the latter, we read out the multivariate normal approximation to the traces of finite families of polynomials in independent complex Wishart matrices.
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作者：Aidekon, Elie
作者单位：Sorbonne Universite; Universite Paris Cite
摘要：We consider a transient random walk (X-n) in random environment on a Galton-Watson tree. Under fairly general assumptions, we give a sharp and explicit criterion for the asymptotic speed to be positive. As a consequence, situations with zero speed are revealed to occur. In such cases, we prove that X-n is of order of magnitude n(Lambda), with Lambda is an element of (0, 1). We also show that the linearly edge reinforced random walk on a regular tree always has a positive asymptotic speed, whic...
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作者：Janvresse, Elise; Rittaud, Benoit; de la Rue, Thierry
作者单位：Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); Universite Paris 13
摘要：We study the random Fibonacci sequences defined by F-1 = F-2 = (F) over tilde (1) = (F) over tilde (2) = 1 and for n >= 1, Fn+2 = Fn+1 +/- F-n (linear case) and (F) over tilde (n+2) = vertical bar(F) over tilde (n+1) +/- (F) over tilde (n)vertical bar (non-linear case), where each +/- sign is independent and either + with probability p or - with probability 1 - p (0 < p <= 1). Our main result is that the exponential growth of F-n for 0 < p <= 1, and of F-n for 0 < p < <= 1, and of (F) over til...
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作者：Kargin, Vladislav
作者单位：New York University
摘要：This paper establishes necessary and sufficient conditions for the sequence of products of freely independent unitary operators to converge in distribution to the uniform law on the unit circle.
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作者：Hughes, C. P.; Nikeghbali, A.; Yor, M.
作者单位：University of York - UK; University of Zurich; Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
摘要：We prove a multidimensional extension of Selberg's central limit theorem for the logarithm of the Riemann zeta function on the critical line. The limit is a totally disordered process, whose coordinates are all independent and Gaussian.
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作者：Tearne, Oliver M.
作者单位：University of Warwick
摘要：This paper concerns comparisons between attractors for random dynamical systems and their corresponding noiseless systems. It is shown that if a random dynamical system has negative time trajectories that are transient or explode with probability one, then the random attractor cannot contain any open set. The result applies to any Polish space and when applied to autonomous stochastic differential equations with additive noise requires only a mild dissipation of the drift. Additionally, follow...
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作者：Janson, Svante; Neininger, Ralph
作者单位：Goethe University Frankfurt; Uppsala University
摘要：We consider the random fragmentation process introduced by Kolmogorov, where a particle having some mass is broken into pieces and the mass is distributed among the pieces at random in such a way that the proportions of the mass shared among different daughters are specified by some given probability distribution (the dislocation law); this is repeated recursively for all pieces. More precisely, we consider a version where the fragmentation stops when the mass of a fragment is below some given...
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作者：Goldsheid, Ilya Ya.
作者单位：University of London
摘要：The main goal of this work is to study the asymptotic behaviour of hitting times of a random walk (RW) in a quenched random environment (RE) on a strip. We introduce enlarged random environments in which the traditional hitting time can be presented as a sum of independent random variables whose distribution functions form a stationary random sequence. This allows us to obtain conditions (stated in terms of properties of random environments) for a linear growth of hitting times of relevant ran...
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作者：Le, H.; Barden, D.
作者单位：University of Nottingham; University of Cambridge
摘要：We generalise, to complete, connected and locally symmetric Riemannian manifolds, the construction of coupled semimartingales X and Y given in Le and Barden (J Lond Math Soc 75: 522 - 544, 2007). When such amanifold has non-negative curvature, this makes it possible for the stochastic anti-development of the corresponding semimartingale exp(Xt) (alpha exp(Xt)(-1)(Y-t)) to be a time-changed Brownian motion with drift when X and Y are. As an application, we use the latter result to strengthen, a...
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作者：Abraham, Romain; Delmas, Jean-Francois
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite de Orleans
摘要：We consider the height process of a Levy process with no negative jumps, and its associated continuous tree representation. Using Levy snake tools developed by Le Gall-Le Jan and Duquesne-Le Gall, with an underlying Poisson process, we construct a fragmentation process, which in the stable case corresponds to the self-similar fragmentation described by Miermont. For the general fragmentation process we compute a family of dislocation measures as well as the law of the size of a tagged fragment...
