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作者：Boutillier, Cedric; de Tiliere, Beatrice
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; University of Neuchatel
摘要：The dimer model on a graph embedded in the torus can be interpreted as a collection of random self-avoiding loops. In this paper, we consider the uniform toroidal honeycomb dimer model. We prove that when the mesh of the graph tends to zero and the aspect of the torus is fixed, the winding number of the collection of loops converges in law to a two-dimensional discrete Gaussian distribution. This is known to physicists in more generality from their analysis of toroidal two-dimensional critical...
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作者：Lytova, A.; Pastur, L.
作者单位：National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine
摘要：We consider n x n real symmetric and Hermitian Wigner random matrices n(-1/2)W with independent (modulo symmetry condition) entries and the (null) sample covariance matrices n(-1) X*X with independent entries of m x n matrix X. Assuming first that the 4th cumulant (excess) kappa(4) of entries of W and X is zero and that their 4th moments satisfy a Lindeberg type condition, we prove that linear statistics of eigenvalues of the above matrices satisfy the central limit theorem (CLT) as n -> infin...
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作者：van Handel, Ramon
作者单位：Princeton University
摘要：We consider a discrete time hidden Markov model where the signal is a stationary Markov chain. When conditioned on the observations, the signal is a Markov chain in a random environment under the conditional measure. It is shown that this conditional signal is weakly ergodic when the signal is ergodic and the observations are nondegenerate. This permits a delicate exchange of the intersection and supremum of or-fields, which is key for the stability of the nonlinear filter and partially resolv...
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作者：Yor, M.
作者单位：Universite Paris Cite; Sorbonne Universite; Universite Paris Cite; Sorbonne Universite; Institut Universitaire de France
摘要：Doob's essential contributions to Probability theory are discussed; this includes the main early results on martingale theory, Doob's h-transform, as well as a summary of Doob's three books. Finally, Doob's 'stochastic triangle' is viewed in the light of the stochastic analysis of the eighties.
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作者：Merkl, Franz; Rolles, Silke W. W.
作者单位：University of Munich; Technical University of Munich
摘要：We consider a linearly edge-reinforced random walk on a class of two-dimensional graphs with constant initial weights. The graphs are obtained from Z(2) by replacing every edge by a sufficiently large, but fixed number of edges in series. We prove that the linearly edge-reinforced random walk on these graphs is recurrent. Furthermore, we derive bounds for the probability that the edge-reinforced random walk hits the boundary of a large box before returning to its starting point.
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作者：Kabluchko, Zakhar; Schlather, Martin; de Haan, Laurens
作者单位：University of Gottingen; Erasmus University Rotterdam - Excl Erasmus MC; Erasmus University Rotterdam
摘要：Let W-i, i is an element of N, be independent copies of a zero-mean Gaussian process {W (t), t is an element of R-d} with stationary increments and variance sigma(2)(t). Independently of W-i, let Sigma(infinity)(i=1) U-delta(i) be a Poisson point process on the real line with intensity e(-y) dy. We show that the law of the random family of functions {V-i(.), i is an element of N}, where V-i(t) = U-i + W-i(t) - sigma(2)(t)/2, is translation invariant. In particular, the process n(t) = V-i=1(inf...
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作者：Sznitman, Alain-Sol
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We study the asymptotic behavior for large N of the disconnection time T(N) of a simple random walk on the discrete cylinder (Z/NZ)(d) x Z, when d >= 2. We explore its connection with the model of random interlacements on Z(d+1) recently introduced in [Ann. Math., in press], and specifically with the percolative properties of the vacant set left by random interlacements. As an application we show that in the large N limit the tail of T(N)/N(2d) is dominated by the tail of the first time when t...
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作者：Cattiaux, Patrick; Collet, Pierre; Lambert, Amaury; Martinez, Servet; Meleard, Sylvie; San Martin, Jaime
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP); Sorbonne Universite; Universite Paris Cite; Universidad de Chile; Universidad de Chile
摘要：In this paper we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to -infinity at the origin, and the diffusion to have an entrance boundary at +infinity. These diffusions arise as images, by a deterministic map, of generalized Feller diffusions, which themselves are obtained as limits of rescaled birth-death processes. Generalized Feller diffusions take nonnegative values and are absorbed at zero in finite time with pr...
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作者：Doob, J. L.
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作者：Pitman, Jim; Winkel, Matthias
作者单位：University of California System; University of California Berkeley; University of Oxford
摘要：We use a natural ordered extension of the Chinese Restaurant Process to grow a two-parameter family of binary self-similar continuum fragmentation trees. We provide an explicit embedding of Ford's sequence of alpha model trees in the continuum tree which we identified in a previous article as a distributional scaling limit of Ford's trees. In general, the Markov branching trees induced by the two-parameter growth rule are not sampling consistent, so the existence of compact limiting trees cann...
