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作者：Blanchet, Jose; Chen, Xinyun; Dong, Jing
作者单位：Columbia University; Wuhan University; Northwestern University
摘要：Consider a multidimensional diffusion process X = {X (t) : t is an element of [0, 1]}. Let epsilon > 0 be a deterministic, user defined, tolerance error parameter. Under standard regularity conditions on the drift and diffusion coefficients of X, we construct a probability space, supporting both X and an explicit, piecewise constant, fully simulatable process X-epsilon such that (sup)(0 <= t <= 1)parallel to X-epsilon (t) - X parallel to(infinity) < epsilon with probability one. Moreover, the ...
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作者：Goldstein, Larry; Nourdin, Ivan; Peccati, Giovanni
作者单位：University of Southern California; University of Luxembourg
摘要：Intrinsic volumes of convex sets are natural geometric quantities that also play important roles in applications, such as linear inverse problems with con, vex constraints, and constrained statistical inference. It is a well-known fact that, given a closed convex cone CC R-d, its conic intrinsic volumes determine a probability measure on the finite set (0, 1,...., d}, customarily denoted by L(V-C). The aim of the present paper is to provide a Berry Esseen bound for the normal approximation of ...
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作者：Jahnel, Benedikt; Kuelske, Christof
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Ruhr University Bochum
摘要：We consider the continuum Widom-Rowlinson model under independent spin-flip dynamics and investigate whether and when the time-evolved point process has an (almost) quasilocal specification (Gibbs-property of the time-evolved measure). Our study provides a first analysis of a Gibbs-non-Gibbs transition for point particles in Euclidean space. We find a picture of loss and recovery, in which even more regularity is lost faster than it is for time-evolved spin models on lattices. We show immediat...
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作者：Yu, Yaming
作者单位：University of California System; University of California Irvine
摘要：Diaconis and Perlman [In Topics in Statistical Dependence (Somerset, PA, 1987) (1990) 147-166, IMS] conjecture that the distribution functions of two weighted sums of i.i.d. gamma random variables cross exactly once if one weight vector majorizes the other. We disprove this conjecture when the shape parameter of the gamma variates is alpha < 1 and prove it when alpha >= 1.
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作者：Dondl, Patrick W.; Scheutzow, Michael
作者单位：University of Freiburg; Technical University of Berlin
摘要：We consider a discretized version of the quenched Edwards-Wilkinson model for the propagation of a driven interface through a random field of obstacles. Our model consists of a system of ordinary differential equations on a d-dimensional lattice coupled by the discrete Laplacian. At each lattice point, the system is subject to a constant driving force and a random obstacle force impeding free propagation. The obstacle force depends on the current state of the solution, and thus renders the pro...
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作者：Etheridge, Alison; Freeman, Nic; Penington, Sarah; Straulino, Daniel
作者单位：University of Oxford; University of Sheffield
摘要：We ask the question when will natural selection on a gene in a spatially structured population cause a detectable trace in the patterns of genetic variation observed in the contemporary population? We focus on the situation in which neighbourhood size, that is the effective local population density, is small. The genealogy relating individuals in a sample from the population is embedded in a spatial version of the ancestral selection graph and through applying a diffusive scaling to this objec...
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作者：Poplavskyi, Mihail; Tribe, Roger; Zaboronski, Oleg
作者单位：University of Warwick
摘要：Let root N + lambda(maX), be the largest real eigenvalue of a random N x N matrix with independent N(0, 1) entries (the real Ginibre matrix). We study the large deviations behaviour of the limiting N -> infinity distribution P[lambda(max) < t] of the shifted maximal real eigenvalue, lambda(max). In particular, we prove that the right tail of this distribution is Gaussian: for t > 0, P[lambda(max) < t] = 1 - 1/4 erfc(t) + O (e(-2t2)). This is a rigorous confirmation of the corresponding result ...
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作者：Li, Yao; Young, Lai-Sang
作者单位：University of Massachusetts System; University of Massachusetts Amherst; New York University
摘要：We consider a stochastic particle system in which a finite number of particles interact with one another via a common energy tank. Interaction rate for each particle is proportional to the square root of its kinetic energy, as is consistent with analogous mechanical models. Our main result is that the rate of convergence to equilibrium for such a system is similar to t(-2), more precisely it is faster than a constant times t(-2+epsilon) for any epsilon > 0. A discussion of exponential vs. poly...
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作者：Aletti, Giacomo; Crimaldi, Irene; Ghiglietti, Andrea
作者单位：University of Milan; IMT School for Advanced Studies Lucca
摘要：Randomly evolving systems composed by elements which interact among each other have always been of great interest in several scientific fields. This work deals with the synchronization phenomenon that could be roughly defined as the tendency of different components to adopt a common behavior. We continue the study of a model of interacting stochastic processes with reinforcement that recently has been introduced in [Crimaldi et al. (2016)]. Generally speaking, by reinforcement we mean any mech...
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作者：Bhattacharya, Bhaswar B.; Diaconis, Persi; Mukherjeet, Sumit
作者单位：University of Pennsylvania; Stanford University; Columbia University
摘要：This paper proves limit theorems for the number of monochromatic edges in uniform random colorings of general random graphs. These can be seen as generalizations of the birthday problem (what is the chance that there are two friends with the same birthday?). It is shown that if the number of colors grows to infinity, the asymptotic distribution is either a Poisson mixture or a Normal depending solely on the limiting behavior of the ratio of the number of edges in the graph and the number of co...
