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作者：Pitman, Jim; Tang, Wenpin
作者单位：University of California System; University of California Berkeley
摘要：Motivated by recent studies of large Mallows(q) permutations, we propose a class of random permutations of N+ and of Z, called regenerative permutations. Many previous results of the limiting Mallows(q) permutations are recovered and extended. Three special examples: blocked permutations, p-shifted permutations and p-biased permutations are studied.
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作者：Benaych-Georges, Florent; Bordenave, Charles; Knowles, Antti
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); University of Geneva
摘要：We consider inhomogeneous Erdos-Renyi graphs. We suppose that the maximal mean degree d satisfies d << log n. We characterise the asymptotic behaviour of the (1-omicron)(n)(1) largest eigenvalues of the adjacency matrix and its centred version. We prove that these extreme eigenvalues are governed at first order by the largest degrees and, for the adjacency matrix, by the nonzero eigenvalues of the expectation matrix. Our results show that the extreme eigenvalues exhibit a novel behaviour which...
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作者：De March, Hadrien; Touzi, Nizar
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：Martingale transport plans on the line are known from Beiglbock and Juillet (Ann. Probab. 44 (2016) 42-106) to have an irreducible decomposition on a (at most) countable union of intervals. We provide an extension of this decomposition for martingale transport plans in R-d, d >= 1. Our decomposition is a partition of R-d consisting of a possibly uncountable family of relatively open convex components, with the required measurability so that the disintegration is well defined. We justify the re...
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作者：Bao, Zhigang; Erdos, Laszlo; Schnelli, Kevin
作者单位：Hong Kong University of Science & Technology; Institute of Science & Technology - Austria; Royal Institute of Technology
摘要：Let U and V be two independent N by N random matrices that are distributed according to Haar measure on U(N). Let Sigma be a nonnegative deterministic N by N matrix. The single ring theorem [Ann. of Math. (2) 174 (2011) 1189-1217] asserts that the empirical eigenvalue distribution of the matrix X : = U Sigma V* converges weakly, in the limit of large N, to a deterministic measure which is supported on a single ring centered at the origin in C. Within the bulk regime, that is, in the interior o...
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作者：Deya, Aurelien
作者单位：Universite de Lorraine
摘要：We study a d-dimensional wave equation model (2 <= d <= 4) with quadratic nonlinearity and stochastic forcing given by a space-time fractional noise. Two different regimes are exhibited, depending on the Hurst parameter H = (H-0, ... , H-d) is an element of (0, 1)(d+1) of the noise: If Sigma(d)(i=0) H-i > d - 1/2, then the equation can be treated directly, while in the case d - 3/4 < Sigma(d)(i=0) H-i <= d - 1/2, the model must be interpreted in the Wick sense, through a renormalization proced...
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作者：Bertoin, Jean; Mallein, Bastien
作者单位：University of Zurich; Universite Paris 13
摘要：We call a random point measure infinitely ramified if for every n is an element of N, it has the same distribution as the nth generation of some branching random walk. On the other hand, branching Levy processes model the evolution of a population in continuous time, such that individuals move in space independently, according to some Levy process, and further beget progenies according to some Poissonian dynamics, possibly on an everywhere dense set of times. Our main result connects these two...
