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作者：Erdos, Laszlo; Knowles, Antti; Yau, Horng-Tzer; Yin, Jun
作者单位：University of Munich; Harvard University; University of Wisconsin System; University of Wisconsin Madison
摘要：We consider the ensemble of adjacency matrices of Erdos-Renyi random graphs, that is, graphs on N vertices where every edge is chosen independently and with probability p equivalent to p(N). We rescale the matrix so that its bulk eigenvalues are of order one. We prove that, as long as pN -> infinity (with a speed at least logarithmic in N), the density of eigenvalues of the Erdos-Renyi ensemble is given by the Wigner semicircle law for spectral windows of length larger than N-1 (up to logarith...
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作者：Hu, Yaozhong; Jolis, Maria; Tindel, Samy
作者单位：University of Kansas; Autonomous University of Barcelona; Universite de Lorraine
摘要：In this article, we derive a Stratonovich and Skorohod-type change of variables formula for a multidimensional Gaussian process with low Holder regularity gamma (typically gamma <= 1/4). To this aim, we combine tools from rough paths theory and stochastic analysis.
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作者：Kwasnicki, Mateusz; Malecki, Jacek; Ryznar, Michal
作者单位：Wroclaw University of Science & Technology; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Universite d'Angers
摘要：In this paper we study the supremum functional M-t = sup(0 <= s <= t) X-s, where X-t, t >= 0, is a one-dimensional Levy process. Under very mild assumptions we provide a simple, uniform estimate of the cumulative distribution function of Mt. In the symmetric case we find an integral representation of the Laplace transform of the distribution of M-t if the Levy-Khintchin exponent of the process increases on (0, infinity).
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作者：Panchenko, Dmitry
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：In many spin glass models, due to the symmetry among sites, any limiting joint distribution of spins under the annealed Gibbs measure admits the Aldous-Hoover representation encoded by a function sigma : [0, 1](4) -> {-1, +1}, and one can think of this function as a generic functional order parameter of the model. In a class of diluted models, and in the Sherrington -Kirkpatrick model, we introduce novel perturbation's of the Hamiltonian that yield certain invariance and self-consistency equat...
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作者：Prokaj, Vilmos
作者单位：Eotvos Lorand University
摘要：The Tanaka equation dX(t) = sign(X-t)dB(t) is an example of a stochastic differential equation (SDE) without strong solution. Hence pathwise uniqueness does not hold for this equation. In this note we prove that if we modify the right-hand side of the equation, roughly speaking, with a strong enough additive noise, independent of the Brownian motion B, then the solution of the obtained equation is pathwise unique.
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作者：Addario-Berry, Louigi; Devroye, Luc; Janson, Svante
作者单位：McGill University; McGill University; Uppsala University
摘要：We study the height and width of a Galton-Watson tree with offspring distribution xi satisfying E xi = 1, 0 < Var xi < infinity, conditioned on having exactly n nodes. Under this conditioning, we derive sub-Gaussian tail bounds for both the width (largest number of nodes in any level) and height (greatest level containing a node); the bounds are optimal up to constant factors in the exponent. Under the same conditioning, we also derive essentially optimal upper tail bounds for the number of no...
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作者：Aidekon, Elie; Hu, Yueyun; Zindy, Olivier
作者单位：Eindhoven University of Technology; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; Universite Paris 13; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Consider a branching random walk on the real line with a killing barrier at zero: starting from a nonnegative point, particles reproduce and move independently, but are killed when they touch the negative half-line. The population of the killed branching random walk dies out almost surely in both critical and subcritical cases, where by subcritical case we mean that the rightmost particle of the branching random walk without killing has a negative speed, and by critical case, when this speed i...
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作者：Baik, Jinho; Jenkins, Robert
作者单位：University of Michigan System; University of Michigan
摘要：The notion of r-crossing and r-nesting of a complete matching was introduced and a symmetry property was proved by Chen et al. [Trans. Amer. Math. Soc. 359 (2007) 1555-1575]. We consider random matchings of large size and study their maximal crossing and their maximal nesting. It is known that the marginal distribution of each of them converges to the GOE Tracy-Widom distribution. We show that the maximal crossing and the maximal nesting becomes independent asymptotically, and we evaluate the ...
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作者：Kargin, V.
作者单位：University of Cambridge
摘要：This paper contributes to the study of the free additive convolution of probability measures. It shows that under some conditions, if measures mu(i) and nu(i), i = 1, 2, are close to each other in terms of the Levy metric and if the free convolution mu(1) boxed plus mu(2) is sufficiently smooth, then nu(1) boxed plus nu(2) is absolutely continuous, and the densities of measures nu(1) boxed plus nu(2) and mu(1) boxed plus mu(2) are close to each other. In particular, convergence in distribution...
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作者：Sen, Arnab; Virag, Balint
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Toronto; University of Toronto
摘要：We show that the top eigenvalue of an n x n random symmetric Toeplitz matrix, scaled by v root 2n log n, converges to the square of the 2 -> 4 operator norm of the sine kernel.
