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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.
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作者：Bobkov, Sergey G.; Chistyakov, Gennadiy P.; Goetze, Friedrich
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Bielefeld
摘要：An Edgeworth-type expansion is established for the entropy distance to the class of normal distributions of sums of i.i.d. random variables or vectors, satisfying minimal moment conditions.
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作者：Basdevant, Anne-Laure; Enriquez, Nathanael; Gerin, Lucas
作者单位：Universite Paris Saclay
摘要：On the supercritical percolation cluster with parameter p, the distances between two distant points of the axis are asymptotically increased by a factor 1 + 1-p/2 + o(1 - p) with respect to the usual distance. The proof is based on an apparently new connection with the TASEP (totally asymmetric simple exclusion process).
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作者：Salisbury, Thomas S.; Sezer, A. Deniz
作者单位：York University - Canada; University of Calgary
摘要：We condition super-Brownian motion on boundary statistics of the exit measure X-D from a bounded domain D. These are random variables defined on an auxiliary probability space generated by sampling from the exit measure X-D. Two particular examples are: conditioning on a Poisson random measure with intensity beta X-D and conditioning on X-D itself. We find the conditional laws as h-transforms of the original SBM law using Dynkin's formulation of X-harmonic functions. We give explicit expressio...
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作者：Adler, Mark; Ferrari, Patrik L.; van Moerbeke, Pierre
作者单位：Brandeis University; University of Bonn
摘要：Consider a continuous time random walk in Z with independent and exponentially distributed jumps +/- 1. The model in this paper consists in an infinite number of such random walks starting from the complement of {-m, -m + 1, ... , m - 1, m} at time -t, returning to the same starting positions at time t, and conditioned not to intersect. This yields a determinantal process, whose gap probabilities are given by the Fredholm determinant of a kernel. Thus this model consists of two groups of rando...
