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作者：Bierme, Hermine; Desolneux, Agnes
作者单位：Universite de Poitiers; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：We introduce the level perimeter integral and the total curvature integral associated with a real-valued function f defined on the plane R-2, as integrals allowing to compute the perimeter of the excursion set of f above level t and the total (signed) curvature of its boundary for almost every level t. Thanks to the Gauss-Bonnet theorem, the total curvature is directly related to the Euler characteristic of the excursion set. We show that the level perimeter and the total curvature integrals c...
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作者：Blanca, Antonio; Gheissari, Reza; Vigoda, Eric
作者单位：University System of Georgia; Georgia Institute of Technology; New York University
摘要：The random-cluster model with parameters (p, q) is a random graph model that generalizes bond percolation (q = 1) and the Ising and Potts models (q >= 2). We study its Glauber dynamics on n x n boxes Lambda(n) of the integer lattice graph Z(2), where the model exhibits a sharp phase transition at p = p(c)(q). Unlike traditional spin systems like the Ising and Potts models, the random-cluster model has non-local interactions. Long-range interactions can be imposed as external connections in the...
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作者：Poisat, Julien; Simenhaus, Francois
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine
摘要：We consider a one-dimensional simple random walk surviving among a field of static soft obstacles: each time it meets an obstacle the walk is killed with probability 1 - e(-beta), where beta is a positive and fixed parameter. The positions of the obstacles are sampled independently from the walk and according to a renewal process. The increments between consecutive obstacles, or gaps, are assumed to have a power-law decaying tail with exponent gamma > 0. We prove convergence in law for the pro...
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作者：Dong, Zhao; Wu, Jiang-Lun; Zhang, Rangrang; Zhang, Tusheng
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Swansea University; Beijing Institute of Technology; University of Manchester
摘要：In this paper, we established the Freidlin-Wentzell-type large deviation principles for first-order scalar conservation laws perturbed by small multiplicative noise. Due to the lack of the viscous terms in the stochastic equations, the kinetic solution to the Cauchy problem for these first-order conservation laws is studied. Then, based on the well-posedness of the kinetic solutions, we show that the large deviations holds by utilising the weak convergence approach.
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作者：Landon, Benjamin; Sosoe, Philippe
作者单位：Massachusetts Institute of Technology (MIT); Cornell University
摘要：We present some applications of central limit theorems on mesoscopic scales for random matrices. When combined with the recent theory of homogenization for Dyson Brownian motion, this yields the universality of quantities which depend on the behavior of single eigenvalues of Wigner matrices and beta-ensembles. Among the results we obtain are the Gaussian fluctuations of single eigenvalues for Wigner matrices (without an assumption of 4 matching moments) and classical beta-ensembles (beta = 1, ...
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作者：Blondel, Oriane; Hilario, Marcelo R.; dos Santos, Renato S.; Sidoravicius, Vladas; Teixeira, Augusto
作者单位：Universite Claude Bernard Lyon 1; Centre National de la Recherche Scientifique (CNRS); Universidade Federal de Minas Gerais; New York University; NYU Shanghai
摘要：We consider a random walker in a dynamic random environment given by a system of independent discrete-time simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on particles. Surprisingly, the random walker may behave very differently depending on whether the underlying environment particles perform lazy or nonlazy random walks, which is related to a notion of permeability of the system. We also provide a st...
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作者：Ernst, P. A.; Peskir, G.; Zhou, Q.
作者单位：Rice University; University of Manchester; Texas A&M University System; Texas A&M University College Station
摘要：Consider the motion of a Brownian particle in three dimensions, whose two spatial coordinates are standard Brownian motions with zero drift, and the remaining (unknown) spatial coordinate is a standard Brownian motion with a (known) nonzero drift. Given that the position of the Brownian particle is being observed in real time, the problem is to detect as soon as possible and with minimal probabilities of the wrong terminal decisions, which spatial coordinate has the nonzero drift. We solve thi...
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作者：Kistler, Nicola; Schertzer, Adrien; Schmidt, Marius A.
作者单位：Goethe University Frankfurt; University of Basel
摘要：This is the second, and last paper in which we address the behavior of oriented first passage percolation on the hypercube in the limit of large dimensions. We prove here that the extremal process converges to a Cox process with exponential intensity. This entails, in particular, that the first passage time converges weakly to a random shift of the Gumbel distribution. The random shift, which has an explicit, universal distribution related to modified Bessel functions of the second kind, is th...
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作者：Shapira, Assaf
作者单位：Universite Paris Cite
摘要：We study two kinetically constrained models in a quenched random environment. The first model is a mixed threshold Fredrickson-Andersen model on Z(2), where the update threshold is either 1 or 2. The second is a mixture of the Fredrickson-Andersen 1-spin facilitated constraint and the North-East constraint in Z(2). We compare three time scales related to these models-the bootstrap percolation time for emptying the origin, the relaxation time of the kinetically constrained model, and the time f...
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作者：Borggaard, Jeff; Glatt-Holtz, Nathan; Krometis, Justin
作者单位：Virginia Polytechnic Institute & State University; Tulane University; Virginia Polytechnic Institute & State University
摘要：We consider the statistical inverse problem of estimating a background fluid flow field v from the partial, noisy observations of the concentration theta of a substance passively advected by the fluid, so that theta is governed by the partial differential equation partial derivative/partial derivative(t )theta (t, x) = - v(x) . del theta(t, x) + kappa Delta theta(t, x), theta(0, x) =theta(0)(x) for t is an element of [0, T], T > 0 and x is an element of T-2 = [0, 1](2). The initial condition t...
