-
作者：Miermont, G
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Sorbonne Universite
摘要：The basic object we consider is a certain model of continuum random tree, called the stable tree. We construct a fragmentation process (F-(t),t greater than or equal to 0) out of this tree by removing the vertices located under height t. Thanks to a self-similarity property of the stable tree, we show that the fragmentation process is also self-similar. The semigroup and other features of the fragmentation are given explicitly. Asymptotic results are given, as well as a couple of related resul...
-
作者：Asselah, A; Castell, F
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：We prove large deviations principles in large time, for the Brownian occupation time in random scenery 1/t integral(0)(t) xi(B-s) ds. The random field is constant on the elements of a partition of R-d into unit cubes. These random constants, say {xi(j), j is an element of Z(d)} consist of i.i.d. bounded variables, independent of the Brownian motion {B-s, s greater than or equal to 0}. This model is a time-continuous version of Kesten and Spitzer's random walk in random scenery. We prove large ...
-
作者：Donati-Martin, C
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We develop a stochastic integration with respect to a q-Brownian motion (for -1 < q < 1), i.e. a non commutative process X, = a, + a(t)* where the operator at and its adjoint fulfill the q commutation relation a(s)a(t)* - qa(t)*a(s) = (S boolean AND t) 1; under the vacuum state expectation. We show that this process enjoys a predictable representation type property.
-
作者：Fagnola, F; Rebolledo, R
作者单位：University of Genoa; Pontificia Universidad Catolica de Chile
摘要：This article introduces a concept of transience and recurrence for a Quantum Markov Semigroup and explores its main properties via the associated potential. We show that an irreducible semigroup is either recurrent or transient and characterize transient semigroups by means of the existence of non trivial superharmonic operators.
-
作者：Götze, F; Tikhomirov, A
作者单位：University of Bielefeld; Syktyvkar State University
摘要：A stochastic bound of order Op(n(-1/2)) for the Kolmogorov distance between the spectral distribution function of an n x n matrix from Wigner ensemble and the distribution function of the semi-circular law is obtained. The result holds assuming that the twelfth moment of the entries of the matrix is uniformly bounded.
-
作者：Tindel, S; Tudor, CA; Viens, E
作者单位：Universite Paris 13; Sorbonne Universite; Purdue University System; Purdue University; Purdue University System; Purdue University
摘要：In this paper linear stochastic evolution equations driven by infinite-dimensional fractional Brownian motion are studied. A necessary and sufficient condition for the existence and uniqueness of the solution is established and the spatial regularity of the solution is analyzed; separate proofs are required for the cases of Hurst parameter above and below 1/2. The particular case of the Laplacian on the circle is discussed in detail.
-
作者：Uzun, HB; Alexander, KS
作者单位：University of Southern California
摘要：We consider boundary roughness for the droplet created when supercritical two-dimensional Bernoulli percolation is conditioned to have an open dual circuit surrounding the origin and enclosing an area at least l(2), for large l. The maximum local roughness is the maximum inward deviation of the droplet boundary from the boundary of its own convex hull; we show that for large l this maximum is at least of order l(1/3) (log l)(-2/3). This complements the upper bound of order l(1/3) (log l)(2/3) ...
-
作者：Bertoin, J; Le Gall, JF
作者单位：Universite Paris Cite; Sorbonne Universite; Sorbonne Universite; Institut Universitaire de France; Universite PSL; Ecole Normale Superieure (ENS)
摘要：We study a class of stochastic flows connected to the coalescent processes that have been studied recently by Mohle, Pitman, Sagitov and Schweinsberg in connection with asymptotic models for the genealogy of populations with a large fixed size. We define a bridge to be a right-continuous process (B(r), r is an element of [0, 1]) with nondecreasing paths and exchangeable increments, such that B(0) = 0 and B(1) = 1. We show that flows of bridges are in one-to-one correspondence with the so-calle...
-
作者：Bogdan, K; Burdzy, K; Chen, ZQ
作者单位：Wroclaw University of Science & Technology; University of Washington; University of Washington Seattle
摘要：We present several constructions of a censored stable process in an open set D subset of R, i.e., a symmetric stable process which is not allowed to jump outside D. We address the question of whether the process will approach the boundary of D in a finite time - we give sharp conditions for such approach in terms of the stability index alpha and the thickness of the boundary. As a corollary, new results are obtained concerning Besov spaces on non-smooth domains, including the critical exponent...
-
作者：Berlinkov, A
作者单位：University of Jyvaskyla
摘要：We explore the exact packing dimension of certain random recursive constructions. In case of polynomial decay at 0 of the distribution function of random variable X, associated with the construction, we prove that it does not exist, and in case of exponential decay it is t(alpha)|log|logt||(beta), where alpha is the fractal dimension of the limit set and 1/beta is the rate of exponential decay.
