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作者：Pfister, CE; Velenik, Y
摘要：We study the 2D Ising model in a rectangular box Lambda(L) of linear size O(L). We determine the exact asymptotic behaviour of the large deviations of the magnetization Sigma(t is an element of Lambda L) sigma(t) when L --> infinity for values of the parameters of the model corresponding to the phase coexistence region, where the order parameter m* is strictly positive. We study in particular boundary effects due to an arbitrary real-valued boundary magnetic field. Using the self-duality of th...
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作者：Kifer, Y
摘要：The study of the Burgers equation with a random force leads via a Hopf-Cole type transformation to a stochastic heat equation having a white noise with spatial parameters type potential. The latter can be studied by means of a general model of directed polymers in random environments with two point random potentials. These models exhibit a Gaussian behavior at large times and have certain stationary distributions which yield the corresponding results for the above stochastic heat and Burgers e...
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作者：Loukianova, D
摘要：This paper contains a first rigorous results at the direction of the converse to Newman's bounds [11] on the storage capacity for the Hopfield model of associative memory. Let m denote the number of stored patterns and N that of neurons, Assuming that m/N --> alpha as N --> infinity we show that for alpha > 0 the memory necessarily commits a positive fraction of errors on memorized patterns that becomes superior to some threshold value (approximately 0.05) as alpha --> infinity.
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作者：Perman, M; Werner, W
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS)
摘要：We study 'perturbed Brownian motions', that can be, loosely speaking, described as follows: they behave exactly as linear Brownian motion except when they hit their past maximum or/and maximum where they get an extra 'push'. We define with no restrictions on the perturbation parameters a process which has this property and show that its law is unique within a certain 'natural class' of processes. In the case where both perturbations (at the maximum and at the minimum) are self-repelling, we sh...
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作者：Doney, RA
摘要：If {S-n, n greater than or equal to 0} is an integer-valued random walk such that S-n/a(n) converges in distribution to a stable law of index alpha is an element of (0, 1) as n --> infinity, then Gnedenko's local limit theorem provides a useful estimate for P{S-n = r} for values of r such that r/a(n) is bounded. The main point of this paper is to show that, under certain circumstances, there is another estimate which is valid when r/a(n) --> +infinity, in other words to establish a large devia...
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作者：Chen, KI; Lo, SH
作者单位：Columbia University
摘要：A simple mapping approach is proposed to study the bootstrap accuracy in a rather general setting. It is demonstrated that the bootstrap accuracy can be obtained through this method for a broad class of statistics to which the commonly used Edgeworth expansion approach may not be successfully applied. We then consider some examples to illustrate how this approach may be used to find the bootstrap accuracy and show the advantage of the bootstrap approximation over the Gaussian approximation. Fo...
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作者：Yau, HT
摘要：Let <(mu)over bar> be a probability measure on the set {0,1,...,R} for some R is an element of N and Lambda(L) a cube of width L in Z(d). Denote by mu(Lambda L)(gc) the (grand canonical) product measure on the configuration space on Lambda(L) with <(mu)over bar> as the marginal measure; here the superscript indicates the grand canonical ensemble. The canonical ensemble, denoted by mu(Lambda L,n)(c), is defined by conditioning mu(Lambda L)(gc) given the total number of particles to be n. Consid...
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作者：Lyons, T; Qian, ZM
摘要：We study two classes of vector fields on the path space over a closed manifold with a Wiener Riemannian measure. By adopting the viewpoint of Yang-Mills field theory, we study a vector field defined by varying a metric connection. We prove that the vector field obtained in this way satisfies a Jacobi field equation which is different from that of classical one by taking in account that a Brownian motion is invariant under the orthogonal group action, so that it is a geometric vector field on t...
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作者：Bentkus, V; Gotze, F
摘要：Let X,X-1,X-2,... be a sequence of i.i.d. random vectors taking values in a d-dimensional real linear space R-d. Assume that EX = 0 and that X is not concentrated in a proper subspace of R-d. Let G denote a mean zero Gaussian random vector with the same covariance operator as that of X. We investigate the distributions of non-degenerate quadratic forms Q[S-N] of the normalized sums S-N = N-1/2(X-1 + ... + X-N) and show that [GRAPHICS] provided that d greater than or equal to 9 and the fourth m...
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作者：Chitashvili, R; Mania, M
摘要：The description of the class of all functions f=(f(t,x), t greater than or equal to 0, x is an element of R) is given, for which the transformed process (f(t, W-t),t greater than or equal to 0) (where W is a standard Wiener process) is a semimartingale.
