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作者：Barbour, A. D.; Luczak, M. J.; Xia, A.
作者单位：University of Zurich; University of London; Queen Mary University London; University of Melbourne
摘要：For integer valued random variables, the translated Poisson distributions form a flexible family for approximation in total variation, in much the same way that the normal family is used for approximation in Kolmogorov distance. Using the Stein-Chen method, approximation can often be achieved with error bounds of the same order as those for the CLT. In this paper, an analogous theory, again based on Stein's method, is developed in the multivariate context. The approximating family consists of ...
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作者：Duits, Maurice
作者单位：Royal Institute of Technology
摘要：We study the global fluctuations for a class of determinantal point processes coming from large systems of non-colliding processes and non-intersecting paths. Our main assumption is that the point processes are constructed by biorthogonal families that satisfy finite term recurrence relations. The central observation of the paper is that the fluctuations of multi-time or multi-layer linear statistics can be efficiently expressed in terms of the associated recurrence matrices. As a consequence,...
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作者：Tang, Wenpin; Tsai, Li-Cheng
作者单位：University of California System; University of California Berkeley; Columbia University
摘要：We study the Up the River problem formulated by Aldous (2002), where a unit drift is distributed among a finite collection of Brownian particles on R+, which are annihilated once they reach the origin. Starting K particles at x = 1, we prove Aldous' conjecture [Aldous (2002)] that the push-the-laggard strategy of distributing the drift asymptotically (as K -> infinity) maximizes the total number of surviving particles, with approximately 4/root pi root K surviving particles. We further establi...
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作者：Barbour, A. D.; Luczak, M. J.; Xia, A.
作者单位：University of Zurich; University of London; Queen Mary University London; University of Melbourne
摘要：The paper applies the theory developed in Part I to the discrete normal approximation in total variation of random vectors in Z(d). We illustrate the use of the method for sums of independent integer valued random vectors, and for random vectors exhibiting an exchangeable pair. We conclude with an application to random colourings of regular graphs.
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作者：Feng, De-Jun; Jarvenpaa, Esa; Jarvenpaa, Maarit; Suomala, Ville
作者单位：Chinese University of Hong Kong; University of Oulu
摘要：Let M, N and K be d-dimensional Riemann manifolds. Assume that A := (A(n))(n is an element of N) is a sequence of Lebesgue measurable subsets of M satisfying a necessary density condition and x := (xn)(n is an element of N) is a sequence of independent random variables, which are distributed on K according to a measure, which is not purely singular with respect to the Riemann volume. We give a formula for the almost sure value of the Hausdorff dimension of random covering sets E(x, A) := lim s...
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作者：Paouris, Grigoris; Valettas, Petros
作者单位：Texas A&M University System; Texas A&M University College Station; University of Missouri System; University of Missouri Columbia
摘要：Let Z be an n-dimensional Gaussian vector and let f : R-n -> R be a convex function. We prove that P(f (Z) <= Ef (Z) - t root Var f(Z) <= = exp(-ct(2)), for all t > 1 where c > 0 is an absolute constant. As an application we derive variance-sensitive small ball probabilities for Gaussian processes.
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作者：van Handel, Ramon
作者单位：Princeton University
摘要：The generic chaining method provides a sharp description of the suprema of many random processes in terms of the geometry of their index sets. The chaining functionals that arise in this theory are however notoriously difficult to control in any given situation. In the first paper in this series, we introduced a particularly simple method for producing the requisite multiscale geometry by means of real interpolation. This method is easy to use, but does not always yield sharp bounds on chainin...
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作者：Champagnat, Nicolas; Jabin, Pierre-Emmanuel
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; University System of Maryland; University of Maryland College Park; University System of Maryland; University of Maryland College Park
摘要：We study strong existence and pathwise uniqueness for stochastic differential equations in R-d with rough coefficients, and without assuming uniform ellipticity for the diffusion matrix. Our approach relies on direct quantitative estimates on solutions to the SDE, assuming Sobolev bounds on the drift and diffusion coefficients, and L-p bounds for the solution of the corresponding Fokker-Planck PDE, which can be proved separately. This allows a great flexibility regarding the method employed to...
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作者：Johansson, Kurt; Lambert, Gaultier
作者单位：Royal Institute of Technology; University of Zurich
摘要：We study mesoscopic linear statistics for a class of determinantal point processes which interpolate between Poisson and random matrix statistics. These processes are obtained by modifying the spectrum of the correlation kernel of the Gaussian Unitary Ensemble (GUE) eigenvalue process. An example of such a system comes from considering the distribution of noncolliding Brownian motions in a cylindrical geometry, or a grand canonical ensemble of free fermions in a quadratic well at positive temp...
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作者：Hairer, M.; Matetski, K.
作者单位：Imperial College London; University of Toronto
摘要：We develop a general framework for spatial discretisations of parabolic stochastic PDEs whose solutions are provided in the framework of the theory of regularity structures and which are functions in time. As an application, we show that the dynamical Phi(4)(3) model on the dyadic grid converges after renormalisation to its continuous counterpart. This result in particular implies that, as expected, the Phi(4)(3) measure with a sufficiently small coupling constant is invariant for this equatio...
