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作者：Simon, T
作者单位：Universite Paris Saclay
摘要：We consider a Brownian bridge on the hyperbolic plane with one extremity tending to infinity, in finite time. We show that the exact exponential rate according-to which this process concentrates around the geodesical segment joining the origin o to the moving extremity z is -rho(o, z), where rho stands for the hyperbolic distance. This improves a result of A. Eberle.
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作者：Maes, C; Redig, F; Saada, E
作者单位：KU Leuven; Eindhoven University of Technology; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider the standard Abelian sandpile process on the Bethe lattice. We show the existence of the thermodynamic limit for the finite volume stationary measures and the existence of a unique infinite volume Markov process exhibiting features of self-organized criticality.
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作者：Bramson, M; Liggett, TM; Mountford, T
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of California System; University of California Los Angeles
摘要：The product Bernoulli measures upsilon(alpha) with densities alpha, alpha is an element of [0, 1], are the extremal translation invariant stationary measures for an exclusion process on Z with irreducible random walk kernel p(.). Stationary measures that are not translation invariant are known to exist for finite range p(.) with positive mean. These measures have particle densities that tend to 1 as x --> infinity and tend to 0 as x --> infinity; the corresponding extremal measures form a onep...
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作者：Bovier, A; Kurkova, I; Löwe, M
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Sorbonne Universite; Radboud University Nijmegen
摘要：We consider the random fluctuations of the free energy in the p-spin version of the Sherrington-Kirkpatrick (SK) model in the high-temperature regime. Using the martingale approach of Comets and Neveu as used in the standard SK model combined with truncation techniques inspired by a recent paper by Talagrand on the p-spin version, we prove that the random corrections to the free energy are on a scale N-(p-2)/2 only and, after proper rescaling, converge to a standard Gaussian random variable. T...
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作者：Dedecker, J; Merlevède, F
作者单位：Sorbonne Universite
摘要：Following Lindeberg's approach, we obtain a new condition for a stationary sequence of square-integrable and real-valued random variables to satisfy the central limit theorem. In the adapted case, this condition is weaker than any projective criterion derived from Gordin's theorem [Dokl. Akad. Nauk SSSR 188 (1969) 739-741] about approximating martingales. Moreover, our criterion is equivalent to the conditional central limit theorem, which implies stable convergence (in the sense of Renyi) to ...
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作者：Matysiak, W; Szablowski, PJ
作者单位：Warsaw University of Technology
摘要：The aim of this note is to reduce a number of assumptions in the recent paper of W. Bryc by showing that some of them imply the others and to give alternative, simpler proofs of some of Bryc's results.
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作者：Campanino, M; Ioffe, D
作者单位：University of Bologna; Technion Israel Institute of Technology
摘要：We derive a precise Ornstein-Zernike asymptotic formula for the decay of the two-point function P-p(0 <----> x) of the Bernoulli bond percolation on the integer lattice Z(d) in any dimension d greater than or equal to 2, in any direction x and for any subcritical value of p < p(c)(d).
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作者：Jiang, TF
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：The maxima of partial sums indexed by squares and rectangles over lattice points and random cubes are studied in this paper. For some of these problems, the dimension (d = 1, d = 2 and d greater than or equal to 3) significantly affects the limit behavior of the maxima. However, for other problems, the maxima behave almost the same as their one-dimensional counterparts. The tools for proving these results are large deviations, the Chen-Stein method, number theory and inequalities of empirical ...
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作者：Fournier, N
作者单位：Universite de Lorraine
摘要：Consider the one-dimensional solution X = {X-t}(tis an element of[0,T]) of a possibly degenerate stochastic differential equation driven by a (non compensated) Poisson measure. We denote by M a set of deterministic integer-valued measures associated with the considered Poisson measure. For in m is an element of M, we denote by S(m) = {S-t(m)}(tis an element of[0,T]) the skeleton associated with X. We assume some regularity conditions, which allow to define a sort of derivative DSt (m) of S-t (...
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作者：Yan, LQ
作者单位：University of British Columbia
摘要：Weak convergence of the Euler scheme for stochastic differential equations is established when coefficients are discontinuous on a set of Lebesgue measure zero. The rate of convergence is presented when coefficients are Holder continuous. Monte Carlo simulations are also discussed.
