-
作者：Calka, P; Schreiber, T
作者单位：Universite Paris Cite; Nicolaus Copernicus University
摘要：In this paper, we are interested in the behavior of the typical Poisson-Voronoi cell in the plane when the radius of the largest disk centered at the nucleus and contained in the cell goes to infinity. We prove a law of large numbers for its number of vertices and the area of the cell outside the disk. Moreover, for the latter, we establish a central limit theorem as well as moderate deviation type results. The proofs deeply rely on precise connections between Poisson-Voronoi tessellations, co...
-
作者：Bass, R; Chen, X; Rosen, J
作者单位：University of Connecticut; University of Tennessee System; University of Tennessee Knoxville; City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：We study large deviations for the renormalized self-intersection on local time of d-dimensional stable processes of index beta is an element of (2d/3,d]. We find a difference between the upper and lower tail. In addition, we find that the behavior of the lower tail depends critically on whether beta < d or beta = d.
-
作者：De Bouard, A; Debussche, A
作者单位：Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay; Universite Paris Saclay
摘要：We study the influence of a multiplicative Gaussian noise, white in time and correlated in space, on the blow-up phenomenon in the supercritical nonlinear Schrodinger equation. We prove that any sufficiently regular and localized deterministic initial data gives rise to a solution which blows up in arbitrarily small time with a positive probability.
-
作者：Kesten, H; Sidoravicius, V
作者单位：Cornell University
摘要：We consider the following interacting particle system: There is a gas of particles, each of which performs a continuous-time simple random walk on Z(d), with jump rate D-A. These particles are called A-particles and move independently of each other. They are regarded as individuals who are ignorant of a rumor or are healthy. We assume that we start the system with N-A (X, 0-) A-particles at x, and that the N-A (X, 0-), x epsilon Z(d), are i.i.d., mean-mu(A) Poisson random variables. In additio...
-
作者：Seppäläinen, T
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：Fluctuations from a hydrodynamic limit of a one-dimensional asymmetric system come at two levels. On the central limit scale n (1/2) one sees initial fluctuations transported along characteristics and no dynamical noise. The second order of fluctuations comes from the particle current across the characteristic. For a system made up of independent random walks we show that the second-order fluctuations appear at scale n (1/4) and converge to a certain self-similar Gaussian process. If the syste...
-
作者：Merkl, F; Rolles, SWW
作者单位：University of Munich; University of Bielefeld
摘要：We prove that the edge-reinforced random walk on the ladder Z x 11, 21 with initial weights a > 3/4 is recurrent. The proof uses a known representation of the edge-reinforced random walk on a finite piece of the ladder as a random walk in a random environment. This environment is given by a marginal of a multicomponent Gibbsian process. A transfer operator technique and entropy estimates from statistical mechanics are used to analyze this Gibbsian process. Furthermore, we prove spatially expon...
-
作者：Maccheroni, F; Marinacci, M
作者单位：Bocconi University; Bocconi University; University of Turin; University of Turin
摘要：We consider a totally monotone capacity on a Polish space and a sequence of bounded p.i.i.d. random variables. We show that, on a full set, any cluster point of empirical averages lies between the lower and the upper Choquet integrals of the random variables, provided either the random variables or the capacity are continuous.
-
作者：Puhalskii, AA
作者单位：University of Colorado System; University of Colorado Denver
摘要：We study the asymptotics of large, moderate and normal deviations for the connected components of the sparse random graph by the method of stochastic processes. We obtain the logarithmic asymptotics of large deviations of the joint distribution of the number of connected components, of the sizes of the giant components and of the numbers of the excess edges of the giant components. For the supercritical case, we obtain the asymptotics of normal deviations and the logarithmic asymptotics of lar...
-
作者：Duquesne, T
作者单位：Universite Paris Saclay
摘要：Let b be an integer greater than I and let W-epsilon = (W-n(epsilon); n > 0) be a random walk on the b-ary rooted tree U-b, starting at the root, going up (resp. down) with probability 1/2 + epsilon (resp. 1/2 - epsilon), epsilon is an element of (0, 1/2), and choosing direction i epsilon {1,...,b) when going up with probability a(i). Here a = (a(1),...,a(b)) stands for some nondegenerated fixed set of weights. We consider the range {W-n(epsilon); n >= 0} that is a subtree Of U-b. It correspon...
-
作者：Konstantinides, DG; Mikosch, T
作者单位：University of Aegean; University of Copenhagen
摘要：In this paper we consider the stochastic recurrence equation Y-t = A(t)Y(t-1) + B-t for an i.i.d. sequence of pairs (A(t), B-t) of nonnegative random variables, where we assume that Bt is regularly varying with index kappa > 0 and EA(t)(kappa) < 1. We show that the stationary solution (Y-t) to this equation has regularly varying finite-dimensional distributions with index K. This implies that the partial sums S-n = Y-1 + - - - + Y-n of this process are regularly varying. In particular, the rel...
