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作者：Birge, Lucien
作者单位：Sorbonne Universite
摘要：We consider here estimation of an unknown probability density belonging to where is a probability measure. We have at hand i.i.d. observations with density and use the squared -norm as our loss function. The purpose of this paper is to provide an abstract but completely general method for estimating by model selection, allowing to handle arbitrary families of finite-dimensional (possibly non-linear) models and any . We shall, in particular, consider the cases of unbounded densities and bounded...
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作者：Campos, David; Ramirez, Alejandro F.
作者单位：Pontificia Universidad Catolica de Chile; Universidad Costa Rica
摘要：We introduce ellipticity criteria for random walks in i.i.d. random environments under which we can extend the ballisticity conditions of Sznitman and the polynomial effective criteria of Berger, Drewitz and Ramirez originally defined for uniformly elliptic random walks. We prove under them the equivalence of Sznitman's condition with the polynomial effective criterion , for large enough. We furthermore give ellipticity criteria under which a random walk satisfying the polynomial effective cri...
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作者：Camia, Federico; Garban, Christophe; Newman, Charles M.
作者单位：Vrije Universiteit Amsterdam; New York University; New York University Abu Dhabi; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON); New York University
摘要：We prove that for the Ising model defined on the plane at the average magnetization under an external magnetic field behaves exactly like The proof, which is surprisingly simple compared to an analogous result for percolation [i.e. that on the triangular lattice (Kesten in Commun Math Phys 109(1):109-156, 1987; Smirnov and Werner in Math Res Lett 8(5-6):729-744, 2001)] relies on the GHS inequality as well as the RSW theorem for FK percolation from Duminil-Copin et al. (Commun Pure Appl Math 64...
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作者：Bobkov, Sergey G.; Chistyakov, Gennadiy P.; Goetze, Friedrich
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Bielefeld
摘要：Berry-Esseen-type bounds for total variation and relative entropy distances to the normal law are established for the sums of non-i.i.d. random variables.
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作者：Li, Xiang-Dong
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Fudan University; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
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作者：Bogachev, Vladimir I.; Roeckner, Michael; Shaposhnikov, Stanislav V.
作者单位：Lomonosov Moscow State University; St Tikhons's University; University of Bielefeld
摘要：We prove absolute continuity of space-time probabilities satisfying certain parabolic inequalities for generators of diffusions with jumps. As an application, we prove absolute continuity of transition probabilities of singular diffusions with jumps under minimal conditions that ensure absolute continuity of the corresponding diffusions without jumps.
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作者：Coquille, Loren; Duminil-Copin, Hugo; Ioffe, Dmitry; Velenik, Yvan
作者单位：University of Geneva; Technion Israel Institute of Technology
摘要：We prove that all Gibbs states of the -state nearest neighbor Potts model on below the critical temperature are convex combinations of the pure phases; in particular, they are all translation invariant. To achieve this goal, we consider such models in large finite boxes with arbitrary boundary condition, and prove that the center of the box lies deeply inside a pure phase with high probability. Our estimate of the finite-volume error term is of essentially optimal order, which stems from the B...
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作者：Lucas, Cyrille
摘要：We build the iDLA cluster using drifted random walks, and study the limiting shapes they exhibit, with the help of sandpile models. For constant drift, the normalised cluster converges to a canonical shape , which can be termed a true heat ball, in that it gives rise to a mean value property for caloric functions. The existence and boundedness of such a shape answers the natural yet open question of the existence and boundedness of a shape that satisfies a mean value property for caloric funct...
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作者：Calka, Pierre; Yukich, J. E.
作者单位：Universite de Rouen Normandie; Lehigh University
摘要：Let be a smooth convex set and let be a Poisson point process on of intensity . The convex hull of is a random convex polytope . As , we show that the variance of the number of -dimensional faces of , when properly scaled, converges to a scalar multiple of the affine surface area of . Similar asymptotics hold for the variance of the number of -dimensional faces for the convex hull of a binomial process in K.
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作者：Restrepo, Ricardo; Shin, Jinwoo; Tetali, Prasad; Vigoda, Eric; Yang, Linji
作者单位：Universidad de Antioquia; University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology
摘要：The hard-core model has received much attention in the past couple of decades as a lattice gas model with hard constraints in statistical physics, a multicast model of calls in communication networks, and as a weighted independent set problem in combinatorics, probability and theoretical computer science. In this model, each independent set I in a graph G is weighted proportionally to lambda(|I|), for a positive real parameter lambda. For large lambda, computing the partition function (namely,...
