-
作者：Csiszár, I; Matús, F
作者单位：Hungarian Academy of Sciences; Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences
摘要：The variation distance closure of an exponential family with a convex set of canonical parameters is described, assuming no regularity conditions. The tools are the concepts of convex core of a measure and extension of an exponential family, introduced previously by the authors, and a new concept of accessible faces of a convex set. Two other closures related to the information divergence are also characterized.
-
作者：Durrett, R; Schweinsberg, J
作者单位：Cornell University; University of California System; University of California San Diego
摘要：Qian, Luscombe and Gerstein [J. Molecular Biol. 313 (2001) 673-681] introduced a model of the diversification of protein folds in a genome that we may formulate as follows. Consider a multitype Yule process starting with one individual in which there are no deaths and each individual gives birth to a new individual at rate 1. When a new individual is born, it has the same type as its parent with probability 1 - r and is a new type, different from all previously observed types, with probability...
-
作者：Lifshits, M; Shi, Z
作者单位：Saint Petersburg State University; Universite Paris Cite; Sorbonne Universite; Universite de Lille
摘要：We consider one-dimensional systems of self-gravitating sticky particles with random initial data and describe the process of aggregation in terms of the largest cluster size L-n at any fixed time prior to the critical time. The asymptotic behavior of L-n is also analyzed for sequences of times tending to the critical time. A phenomenon of phase transition shows up, namely, for small initial particle speeds (cold gas) L-n has logarithmic order of growth while higher speeds (warm gas) yield pol...
-
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.
