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作者：Najnudel, Joseph
作者单位：University of Zurich
摘要：In this article, we prove that the measures Q(T) associated to the one-dimensional Edwards' model on the interval [0. T] converge to a limit measure Q when T goes to infinity, in the following sense: for all s >= 0 and for all events A(s) depending on the canonical process only up to time s, Q(T) (A(s)) Q(A(s)). Moreover, we prove that, if P is Wiener measure, there exists a martingale (D-s)(s is an element of R+) such that Q(A(s)) = E-P(1(As) D-s), and we give an explicit expression for this ...
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作者：Farre, Merce; Jolis, Maria; Utzet, Frederic
作者单位：Autonomous University of Barcelona
摘要：In the framework of vector measures and the combinatorial approach to stochastic multiple integral introduced by Rota and Wallstrom [Ann. Probab. 25 (1997) 1257-1283], we present an Ito multiple integral and a Stratonovich multiple integral with respect to a Levy process with finite moments up to a convenient order. In such a framework, the Stratonovich multiple integral is an integral with respect to a product random measure whereas the Ito multiple integral corresponds to integrate with resp...
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作者：Peterson, Jonathon; Seppaelaeinen, Timo
作者单位：Cornell University; University of Wisconsin System; University of Wisconsin Madison
摘要：We study the current of particles that move independently in a common static random environment on the one-dimensional integer lattice. A two-level fluctuation picture appears. On the central limit scale the quenched mean of the current process converges to a Brownian motion. On a smaller scale the current process centered at its quenched mean converges to a mixture of Gaussian processes. These Gaussian processes are similar to those arising from classical random walks, but the environment mak...
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作者：Gnedin, Alexander; Olshanskii, Grigori
作者单位：Utrecht University; Kharkevich Institute for Information Transmission Problems of the RAS
摘要：For positive q not equal 1, the q-exchangeability of an infinite random word is introduced as quasi-invariance under permutations of letters, with a special cocycle which accounts for inversions in the word. This framework allows us to extend the q-analog of de Finetti's theorem for binary sequences-see Gresehonig and Schmidt [Colloq. Math. 84/85 (2000) 495-514]-to general real-valued sequences. In contrast to the classical case of exchangeability (q = 1), the order on R plays a significant ro...
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作者：Chatterjee, Sourav; Dey, Partha S.
作者单位：University of California System; University of California Berkeley
摘要：Stein's method for concentration inequalities was introduced to prove concentration of measure in problems involving complex dependencies such as random permutations and Gibbs measures. In this paper, we provide some extensions of the theory and three applications: (1) We obtain a concentration inequality for the magnetization in the Curie-Weiss model at critical temperature (where it obeys a nonstandard normalization and super-Gaussian concentration). (2) We derive exact large deviation asymp...
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作者：Joulin, Alderic; Ollivier, Yann
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：We provide explicit nonasymptotic estimates for the rate of convergence of empirical means of Markov chains, together with a Gaussian or exponential control on the deviations of empirical means. These estimates hold under a positive curvature assumption expressing a kind of metric ergodicity, which generalizes the Ricci curvature from differential geometry and, on finite graphs, amounts to contraction under path coupling.
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作者：Nystrom, Kaj; Onskog, Thomas
作者单位：Umea University
摘要：The deterministic Skorohod problem plays an important role in the construction and analysis of diffusion processes with reflection. In the form studied here, the multidimensional Skorohod problem was introduced, in time-independent domains, by H. Tanaka [61] and further investigated by P.-L. Lions and A.-S. Sznitman [42] in their celebrated article. Subsequent results of several researchers have resulted in a large literature on the Skorohod problem in time-independent domains. In this article...
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作者：Sadel, Christian; Schulz-Baldes, Hermann
作者单位：University of Erlangen Nuremberg
摘要：A random Lie group action on a compact manifold generates a discrete time Markov process. The main object of this paper is the evaluation of associated Birkhoff sums in a regime of weak, but sufficiently effective coupling of the randomness. This effectiveness is expressed in terms of random Lie algebra elements and replaces the transience or Furstenberg's irreducibility hypothesis in related problems. The Birkhoff sum of any given smooth function then turns out to be equal to its integral w.r...
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作者：Caravenna, Francesco; Giacomin, Giambattista
作者单位：University of Padua; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
摘要：A copolymer is a chain of repetitive units (monomers) that are almost identical, but they differ in their degree of affinity for certain solvents. This difference leads to striking phenomena when the polymer fluctuates in a non-homogeneous medium, for example, made of two solvents separated by an interface. One may observe, for instance, the localization of the polymer at the interface between the two solvents. A discrete model of such system, based on the simple symmetric random walk on Z, ha...
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作者：Barlow, Martin T.; Masson, Robert
作者单位：University of British Columbia
摘要：Let M(n) be the number of steps of the loop-erasure of a simple random walk on Z(2) from the origin to the circle of radius n. We relate the moments of M(n) to Es(n), the probability that a random walk and an independent loop-erased random walk both started at the origin do not intersect up to leaving the ball of radius n. This allows us to show that there exists C such that for all n and all k = 1,2,..., E[M(n)(k)] <= C(k)k!E[M(n)](k) and hence to establish exponential moment bounds for M(n)....
