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作者：Dey, Partha s.; Terlov, G. R. I. G. O. R. Y.
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：In the seventies, Charles Stein revolutionized the way of proving the cen-tral limit theorem by introducing a method that utilizes a characterization equation for Gaussian distribution. In the last 50 years, much research has been done to adapt and strengthen this method to a variety of different set-tings and other limiting distributions. However, it has not been yet extended to study conditional convergences. In this article we develop a novel approach, using Stein's method for exchangeable ...
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作者：Cordero-Erausquin, Dario; Rotem, Liran
作者单位：Sorbonne Universite; Universite Paris Cite; Technion Israel Institute of Technology
摘要：We prove that the (B) conjecture and the Gardner-Zvavitch conjecture are true for all log-concave measures that are rotationally invariant, extend-ing previous results known for Gaussian measures. Actually, our result apply beyond the case of log-concave measures, for instance, to Cauchy measures as well. For the proof, new sharp weighted Poincare inequalities are obtained for even probability measures that are log-concave with respect to a rotation-ally invariant measure.
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作者：Dereudre, David; Vasseur, Thibaut
作者单位：Universite de Lille; Universite Paris Cite
摘要：For an inverse temperature /3 > 0, we define the /3-circular Riesz gas on Rd as any microscopic thermodynamic limit of Gibbs particle systems on the torus interacting via the Riesz potential g(x) = IlxII-s. We focus on the nonintegrable case d -1 < s < d. Our main result ensures, for any dimension d > 1 and inverse temperature /3 > 0, the existence of a /3-circular Riesz gas which is not number-rigid. Recall that a point process is said number rigid if the number of points in a bounded Borel s...
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作者：Xiao, Hui; Grama, Ion; Liu, Quansheng
作者单位：Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Consider (gn)n>1 a sequence of independent and identically distributed random matrices and the left random walk Gn := gn . . . g1, n > 1 on the general linear group GL(d, R). Under suitable conditions we establish a Bahadur-Rao-Petrov type large deviation expansion for the coefficient (f, Gnv) of the product Gn, where v & epsilon; Rd and f & epsilon; (Rd)*. In particular, we obtain an explicit rate function in the large deviation principle, thus im-proving significantly the known large deviati...
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作者：Conchon-Kerjan, Guillaume; Goldschmidt, Christina
作者单位：University of Bath; University of Oxford
摘要：We prove a metric space scaling limit for a critical random graph with independent and identically distributed degrees having power-law tail be-haviour with exponent alpha + 1, where alpha & ISIN; (1, 2). The limiting components are constructed from random R-trees encoded by the excursions above its run-ning infimum of a process whose law is locally absolutely continuous with respect to that of a spectrally positive alpha-stable Levy process. These spanning R-trees are measure-changed alpha-st...
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作者：Cuny, C.; Dedecker, J.; Merlevede, F.; Peligrad, M.
作者单位：Universite de Bretagne Occidentale; Universite Paris Cite; Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); University System of Ohio; University of Cincinnati
摘要：Let A(n) = epsilon(n) center dot center dot center dot epsilon(1), where (epsilon n)n >= 1 is a sequence of independent random matrices, taking values in GL(d)(R), d >= 2, with common distribution mu. In this paper, under standard assumptions on mu (strong irreducibility and prox-imality) we prove Berry-Esseen type theorems for log(||A(n)||) when mu has a polynomial moment. More precisely, we get the rate ((logn)/n)(q/2-1), when mu has a moment of order q is an element of[2, 3] and the rate 1/...
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作者：Landim, C.; Marcondes, D.; Seo, I
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA); Universite de Rouen Normandie; Universidade de Sao Paulo; Seoul National University (SNU); Seoul National University (SNU)
摘要：We present a general method to derive the metastable behavior of weakly mixing Markov chains. This approach is based on properties of the resolvent equations and can be applied to metastable dynamics, which do not satisfy the As an application, we study the metastable behavior of critical zero-range processes. Let r : S x S -> R+ be the jump rates of an irreducible random walk on a finite set S, reversible with respect to the uniform measure. For alpha > 0, let g : N -> R+ be given by g(0) = 0...
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作者：Bobkov, Sergey G.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Upper pointwise bounds are considered for convolution of bounded densities in terms of the associated Laplace and Legendre transforms. Applications of these bounds are illustrated in the central limit theorem with respect to the Renyi divergence.
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作者：Chelkak, Dmitry; Izyurov, Konstantin; Mahfouf, Remy
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; University of Helsinki
摘要：We prove universality of spin correlations in the scaling limit of the planar Ising model on isoradial graphs with uniformly bounded angles and Z-invariant weights. Specifically, we show that in the massive scaling limit, that is, as the mesh size tends to zero at the same rate as the Baxter elliptic parameter tends to 1, the two-point spin correlations in the full plane converge to a universal rotationally invariant limit. These results, together with techniques developed to obtain them, are ...
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作者：Landon, Benjamin; Noack, Christian; Sosoe, Philippe
作者单位：University of Toronto; Purdue University System; Purdue University; Cornell University
摘要：We consider systems of N diffusions in equilibrium interacting through a potential V. We study a height function, which, for the special choice V (x) = e(-x), coincides with the partition function of a stationary semidis-crete polymer, also known as the (stationary) O'Connell-Yor polymer. For a general class of smooth convex potentials (generalizing the O'Connell-Yor case), we obtain the order of fluctuations of the height function by proving matching upper , lower bounds for the variance of o...
