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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...
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作者：Nutz, Marcel; Wiesel, Johannes
作者单位：Columbia University; Columbia University
摘要：We study the stability of entropically regularized optimal transport with respect to the marginals. Given marginals converging weakly, we establish a strong convergence for the Schr delta dinger potentials, describing the density of the optimal couplings. When the marginals converge in total variation, the optimal couplings also converge in total variation. This is applied to show that Sinkhorn's algorithm converges in total variation when costs are quadratic and marginals are subgaussian or, ...
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作者：Comets, Francis; Dalmau, Joseba; Saglietti, Santiago
作者单位：Universite Paris Cite; New York University; NYU Shanghai; Pontificia Universidad Catolica de Chile
摘要：Ballistic deposition is a classical model for interface growth in which unit blocks fall down vertically at random on the different sites of Z and stick to the interface at the first point of contact, causing it to grow. We consider an alternative version of this model in which the blocks have random heights which are i.i.d. and heavy tailed, and where each block sticks to the interface at the first point of contact with probability p (otherwise, it falls straight down until it lands on a bloc...
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作者：Angel, Omer; Holmes, Mark; Ramirez, Alejandro
作者单位：University of British Columbia; University of Melbourne; New York University; NYU Shanghai; Pontificia Universidad Catolica de Chile
摘要：We give nontrivial upper and lower bounds on the range of the so-called Balanced Excited Random Walk in two dimensions and verify a conjecture of Benjamini, Kozma and Schapira. To the best of our knowledge, these are the first nontrivial results for this two-dimensional model.
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作者：Janson, Svante; Louf, Baptiste
作者单位：Uppsala University
摘要：We study uniformly random maps with a single face, genus g, and size n, as n, g -infinity with g = o(n), in continuation of several previous works on the geometric properties of high genus maps. We calculate the number of short simple cycles, and we show convergence of their lengths (after a well-chosen rescaling of the graph distance) to a Poisson process, which happens to be exactly the same as the limit law obtained by Mirzakhani and Petri (Comment. Math. Helv. 94 (2019) 869-889) when they ...
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作者：Jaramillo, Arturo; Nourdin, Ivan; Nualart, David; Peccati, Giovanni
作者单位：CIMAT - Centro de Investigacion en Matematicas; University of Luxembourg; University of Kansas
摘要：We investigate first and second order fluctuations of additive functionals of a fractional Brownian motion (fBm) of the form [GRAPHICS] . where B={B-t; t >= 0} is a fBm with Hurst parameter H is an element of(0,1), f is a suitable test function and lambda is an element of R. We develop our study by distinguishing two regimes which exhibit different behaviors. When H is an element of(0,1/3), we show that a suitable renormalization of (0.1), compensated by a multiple of the local time of B, conv...
