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作者：Cerf, R.; Messikh, R. J.
作者单位：Universite Paris Saclay; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We study the 2D-Ising model defined on finite boxes at temperatures that are below but very close from the critical point. When the temperature approaches the critical point and the size of the box grows fast enough, we establish large deviations estimates on FK-percolation events that concern the phenomenon of phase coexistence.
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作者：Damron, Michael; Sapozhnikov, Artem
作者单位：Princeton University
摘要：We study invasion percolation in two dimensions, focusing on properties of the outlets of the invasion and their relation to critical percolation and to incipient infinite clusters (IICs). First we compute the exact decay rate of the distribution of both the weight of the kth outlet and the volume of the kth pond. Next we prove bounds for all moments of the distribution of the number of outlets in an annulus. This result leads to almost sure bounds for the number of outlets in a box B(2 (n) ) ...
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作者：Mirek, Mariusz
作者单位：University of Wroclaw
摘要：We consider the Markov chain {X-n(x)}(n=0)(infinity) = 0 on R-d defined by the stochastic recursion X-n(x) = psi(theta n) (X-n-1(x)), starting at x is an element of R-d, where theta(1), theta(2), ... are i.i.d. random variables taking their values in a metric space (Theta, r), and psi(theta n) : R-d -> R-d are Lipschitz maps. Assume that theMarkov chain has a unique stationary measure.. Under appropriate assumptions on psi(theta n) , we will show that the measure. has a heavy tail with the exp...
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作者：Banica, Teodor; Curran, Stephen; Speicher, Roland
作者单位：CY Cergy Paris Universite; University of California System; University of California Berkeley; Queens University - Canada
摘要：We consider several orthogonal quantum groups satisfying the easiness assumption axiomatized in our previous paper. For each of them we discuss the computation of the asymptotic law of Tr(u (k) ) with respect to the Haar measure, u being the fundamental representation. For the classical groups O (n) , S (n) we recover in this way some well-known results of Diaconis and Shahshahani.
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作者：Chen, Xin; Li, Xue-Mei; Wu, Bo
作者单位：University of Warwick; University of Warwick
摘要：The aim of the paper is to study the pinned Wiener measure on the loop space over a simply connected compact Riemannian manifold together with a Hilbert space structure and the Ornstein-Uhlenbeck operator d*d. We give a concrete estimate for the weak Poincar, inequality, assuming positivity of the Ricci curvature of the underlying manifold. The order of the rate function is s (-alpha) for any alpha > 0.
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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
摘要：Based on a new martingale representation formula, we prove some quantitative upper bound estimates of the L (p) -norm of some singular integral operators on complete Riemannian manifolds. This leads us to establish the Weak L (p) -Hodge decomposition theorem and to prove the L (p) -boundedness of the Beurling-Ahlfors transforms on complete non-compact Riemannian manifolds with non-negative Weitzenbock curvature operator.
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作者：Daskalakis, Constantinos; Mossel, Elchanan; Roch, Sebastien
作者单位：University of California System; University of California Los Angeles; Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley; Weizmann Institute of Science
摘要：A major task of evolutionary biology is the reconstruction of phylogenetic trees from molecular data. The evolutionary model is given by a Markov chain on a tree. Given samples from the leaves of the Markov chain, the goal is to reconstruct the leaf-labelled tree. It is well known that in order to reconstruct a tree on n leaves, sample sequences of length Omega (log n) are needed. It was conjectured by Steel that for the CFN/Ising evolutionary model, if the mutation probability on all edges of...
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作者：Buchmann, Boris; Maller, Ross
作者单位：Monash University; Australian National University
摘要：We give a small time functional version of Chung's other law of the iterated logarithm for L,vy processes with non-vanishing Brownian component. This is an analogue of the other law of the iterated logarithm at large times for L,vy processes and random walks with finite variance, as extended to a functional version by Wichura. As one of many possible applications, we mention a functional law for a two-sided passage time process.
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作者：Baraud, Yannick
作者单位：Universite Cote d'Azur
摘要：We observe a random measure N and aim at estimating its intensity s. This statistical framework allows to deal simultaneously with the problems of estimating a density, the marginals of a multivariate distribution, the mean of a random vector with nonnegative components and the intensity of a Poisson process. Our estimation strategy is based on estimator selection. Given a family of estimators of s based on the observation of N, we propose a selection rule, based on N as well, in view of selec...
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作者：Nandori, Peter
作者单位：Budapest University of Technology & Economics
摘要：In the classical paper of Dvoretzky and ErdAs (Proceedings of the 2nd Berkeley Symposium on Mathematical Statistics and Probability, pp 353-367, 1951), asymptotics for the expected value and the variance of the number of distinct sites visited by a Simple Symmetric Random Walk were calculated. Here, these results are generalized for Random Walks with Internal States. Moreover, both weak and strong laws of large numbers are proved. As a tool for these results, the error term of the local limit ...
