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作者：Bramson, Maury; Burdzy, Krzysztof; Kendall, Wilfrid
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Washington; University of Washington Seattle; University of Warwick
摘要：Two random processes X and Y on a metric space are said to be epsilon-shy coupled if there is positive probability of them staying at least a positive distance E apart from each other forever. Interest in the literature centres on nonexistence results subject to topological and geometric conditions; motivation arises from the desire to gain a better understanding of probabilistic coupling. Previous nonexistence results for co-adapted shy coupling of reflected Brownian motion required convexity...
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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：Huesmann, Martin; Sturm, Karl-Theodor
作者单位：University of Bonn
摘要：This paper is devoted to the study of couplings of the Lebesgue measure and the Poisson point process. We prove existence and uniqueness of an optimal coupling whenever the asymptotic mean transportation cost is finite. Moreover, we give precise conditions for the latter which demonstrate a sharp threshold at d = 2. The cost will be defined in terms of an arbitrary increasing function of the distance. The coupling will be realized by means of a transport map (allocation map) which assigns to e...
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作者：Anderson, Greg W.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：For polynomials in independent Wigner matrices, we prove convergence of the largest singular value to the operator norm of the corresponding polynomial in free semicircular variables, under fourth moment hypotheses. We actually prove a more general result of the form no eigenvalues outside the support of the limiting eigenvalue distribution. We build on ideas of Haagerup-Schultz-Thorbjornsen on the one hand and Bai-Silverstein on the other. We refine the linearization trick so as to preserve s...
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作者：Chaumont, L.
作者单位：Universite d'Angers
摘要：We show that the law of the overall supremum (X) over bar (t) = sup(s <= t) X-s of a Levy process X, before the deterministic time t is equivalent to the average occupation measure mu(+)(t) (dx) = integral(t)(0))P(X-s is an element of dx) ds, whenever 0 is regular for both open halflines (-infinity, 0) and (0, infinity). In this case, P((X) over bar (t) is an element of dx) is absolutely continuous for some (and hence for all) t > 0 if and only if the resolvent measure of X is absolutely conti...
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作者：Schreiber, Tomasz; Thaele, Christoph
作者单位：Nicolaus Copernicus University; University Osnabruck
摘要：The intent of this paper is to describe the large scale asymptotic geometry of iteration stable (STIT) tessellations in R-d, which form a rather new, rich and flexible class of random tessellations considered in stochastic geometry. For this purpose, martingale tools are combined with second-order formulas proved earlier to establish limit theorems for STIT tessellations. More precisely, a Gaussian functional central limit theorem for the surface increment process induced a by STIT tessellatio...
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作者：Miller, Jason
作者单位：Stanford University
摘要：Let X-1, X-2 be independent random walks on Z(n)(d), d >= 3, each starting from the uniform distribution. Initially, each site of Z(n)(d) is unmarked, and, whenever X-i visits such a site, it is set irreversibly to i. The mean of vertical bar A(i)vertical bar, the cardinality of the set A(i) of sites painted by i, once all of Z(n)(d) has been visited, is 1/2n(d) by symmetry. We prove the following conjecture due to Pemantle and Peres: for each d >= 3 there exists a constant alpha(d) such that ...
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作者：Cont, Rama; Fournie, David-Antoine
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Columbia University
摘要：We develop a nonanticipative calculus for functionals of a continuous semimartingale, using an extension of the Ito formula to path-dependent functionals which possess certain directional derivatives. The construction is based on a pathwise derivative, introduced by Dupire, for functionals on the space of right-continuous functions with left limits. We show that this functional derivative admits a suitable extension to the space of square-integrable martingales. This extension defines a weak d...
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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).
