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作者：Kabluchko, Zakhar; Zaporozhets, Dmitry
作者单位：Ulm University; Russian Academy of Sciences
摘要：It has been shown by Ibragimov and Zaporozhets [In Prokhorov and Contemporary Probability Theory (2013) Springer] that the complex roots of a random polynomial G(n)(z) = Sigma(n)(k=0) xi(k)z(k) with i.i.d. coefficients xi(0), ... , xi(n) concentrate a.s. near the unit circle as n -> infinity if and only if E log(+)vertical bar xi(0)vertical bar < infinity. We study the transition from concentration to deconcentration of roots by considering coefficients with tails behaving like L(log vertical ...
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作者：Samorodnitsky, Gennady; Shen, Yi
作者单位：Cornell University
摘要：It is, perhaps, surprising that the location of the unique supremum of a stationary process on an interval can fail to be uniformly distributed over that interval. We show that this distribution is absolutely continuous in the interior of the interval and describe very specific conditions the density has to satisfy. We establish universal upper bounds on the density and demonstrate their optimality.
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作者：Dedecker, Jerome; Merlevede, Florence; Rio, Emmanuel
作者单位：Universite Paris Cite; Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also holds for the empirical process associated to iterates of expanding maps with a neutral fixed point at zero, as soon as the correlations decrease more rapidly than n(-1-delta) for some positive delta. This shows that our conditions are in some sense optimal.
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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：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：Fukushima, Ryoki
作者单位：Institute of Science Tokyo; Tokyo Institute of Technology
摘要：Consider a d-dimensional Brownian motion in a random potential defined by attaching a nonnegative and polynomially decaying potential around Poisson points. We introduce a repulsive interaction between the Brownian path and the Poisson points by weighting the measure by the Feynman-Kac functional. We show that under the weighted measure, the Brownian motion tends to localize around the origin. We also determine the scaling limit of the path and also the limit shape of the random potential.
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作者：Redig, Frank; Voellering, Florian
作者单位：Delft University of Technology; University of Gottingen
摘要：We study a general class of random walks driven by a uniquely ergodic Markovian environment. Under a coupling condition on the environment we obtain strong ergodicity properties for the environment as seen from the position of the walker, that is, the environment process. We can transfer the rate of mixing in time of the environment to the rate of mixing of the environment process with a loss of at most polynomial order. Therefore the method is applicable to environments with sufficiently fast...
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作者：Fresen, Daniel
作者单位：Yale University
摘要：We show that the convex hull of a large i.i.d. sample from an absolutely continuous log-concave distribution approximates a predetermined convex body in the logarithmic Hausdorff distance and in the Banach-Mazur distance. For log-concave distributions that decay super-exponentially, we also have approximation in the Hausdorff distance. These results are multivariate versions of the Gnedenko law of large numbers, which guarantees concentration of the maximum and minimum in the one-dimensional c...
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作者：Gozlan, N.; Roberto, C.; Samson, P. -M.
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel
摘要：We give a characterization of transport-entropy inequalities in metric spaces. As an application we deduce that such inequalities are stable under bounded perturbation (Holley-Stroock perturbation lemma).
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作者：Da Prato, G.; Flandoli, F.; Priola, E.; Roeckner, M.
作者单位：Scuola Normale Superiore di Pisa; University of Pisa; University of Turin; University of Bielefeld
摘要：We prove pathwise (hence strong) uniqueness of solutions to stochastic evolution equations in Hilbert spaces with merely measurable bounded drift and cylindrical Wiener noise, thus generalizing Veretennikov's fundamental result on R-d to infinite dimensions. Because Sobolev regularity results implying continuity or smoothness of functions do not hold on infinite-dimensional spaces, we employ methods and results developed in the study of Malliavin-Sobolev spaces in infinite dimensions. The pric...
