-
作者：Bernyk, Violetta; Dalang, Robert C.; Peskir, Goran
作者单位：University of Cambridge; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Manchester
摘要：Let X = (X-t)(t >= 0) be a stable Levy process of index alpha is an element of (1.2) with no negative jumps and let S-t = sup(0 <= s <= 1) X-s denote its running spremum for t > 0. We show that the density funtion f(1) of S-1 can be characterized as the unique solution to a weakly singular Voleterra integral equation of the first kind or equivalently, as the unique solution to a first-order Riemann-Liouville fractional differential equation satisfying a boundry condition at zero. This yeilds a...
-
作者：Campanino, Massimo; Ioffe, Dmitry; Velenik, Yvan
作者单位：University of Bologna; University of Geneva
摘要：We develop a fluctuation theory of connectivities for subcritical random cluster models. The theory is based on a comprehensive nonperturbative probabilistic description of long connected clusters in terms of essentially one-dimensional chains of irreducible objects. Statistics of local observables, for example, displacement, over such chains obey classical limit laws, and our construction leads to an effective random walk representation of percolation clusters. The results include a derivatio...
-
作者：Roitershtein, Alexander
作者单位：Iowa State University
摘要：We consider transient random walks on a strip in a random environment. The model was introduced by Bolthausen and Goldsheid [Comm. Math. Phys. 214 (2000) 429-447]. We derive a strong law of large numbers for the random walks in a general ergodic setup and obtain an annealed central limit theorem in the case of uniformly mixing environments. In addition, we prove that the law of the environment viewed from the position of the walker converges to a limiting distribution if the environment is an ...
-
作者：Bezerra, Sergio; Tindel, Samy; Viens, Frederi
作者单位：Universite de Lorraine; Purdue University System; Purdue University
摘要：This paper provides information about the asymptotic behavior of a one-dimensional Brownian polymer ill random medium represented by a Gaussian field W on R+ x R which is white noise in time and function-valued space. According to the behavior of the spatial covariance of W, we give a lower bound on the power growth (wandering exponent) of the polymer when the time parameter goes to infinity: the polymer is proved to be superdiffusive, with a wandering exponent exceeding any alpha < 3/5.
-
作者：Collins, Benoit; Stolz, Michael
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; University of Ottawa; Ruhr University Bochum
摘要：We study random vectors of the form (Tr(A((1))V),...,Tr(A((r))V)), where V is a uniformly distributed element of a matrix version of a classical compact symmetric space, and the AM are deterministic parameter matrices. We show that for increasing matrix sizes these random vectors converge to a joint Gaussian limit, and compute its covariances. This generalizes previous work of Diaconis et al. for Haar distributed matrices from the classical compact groups. The proof uses integration formulas, ...
-
作者：Goergen, Laurent
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：In the setting of multidimensional diffusions in random environment, we carry on the investigation of condition (T'), introduced by Sznitman [Ann. Probab. 29 (2001) 723-764] and by Schmitz [Ann. Inst. H. Poincare Probab. Statist. 42 (2006) 683-714] respectively in the discrete and continuous setting, and which implies a law of large numbers with nonvanishing limiting velocity (ballistic behavior) as well as a central limit theorem. Specifically, we show that when d >= 2, (V) is equivalent to a...
-
作者：Angel, Omer; Goodman, Jesse; Den Hollander, Frank; Slade, Gordon
作者单位：University of Toronto; University of British Columbia; Leiden University; Leiden University - Excl LUMC
摘要：We consider invasion percolation on a rooted regular tree. For the infinite cluster invaded from the root, we identify the scaling behavior of its r-point function for any r >= 2 and of its volume both at a given height and below a given height. We find that while the power laws of the scaling are the same as for the incipient infinite cluster for ordinary percolation, the scaling functions differ. Thus, somewhat surprisingly, the two clusters behave differently; in fact, we prove that their l...
-
作者：Chistyakov, G. P.; Goetze, F.
作者单位：National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine; University of Bielefeld
摘要：Based on an analytical approach to the definition of additive free convolution on probability measures on the real line, we prove free analogues of limit theorems for sums for nonidentically distributed random variables in classical probability theory.
-
作者：Pellegrini, Clement
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：Recent developments in quantum physics make heavy use of so-called quantum trajectories. Mathematically, this theory gives rise to stochastic Schrodinger equations, that is, perturbation of Schrodinger-type equations under the form of stochastic differential equations. But Such equations are in general not of the usual type as considered in the literature. They pose a serious problem in terms of justifying the existence and uniqueness of a Solution, Justifying the physical pertinence of the eq...
-
作者：Nachmias, Asaf; Peres, Yuval
作者单位：University of California System; University of California Berkeley; Microsoft
摘要：Let C-1 denote the largest connected component of the critical Erdos-Renyi random graph G(n, 1/n). We show that, typically, the diameter of C-1 is of order n(1/3) and the mixing time of the lazy simple random walk on C-1 is of order n. The latter answers a question of Benjamini, Kozma and Wormald. These results extend to clusters of size n(2/3) of p-bond percolation on any d-regular n-vertex graph where such clusters exist, provided that p(d-1) <= 1 + O(n(-1/3)).
