Galton-Watson process. (Proceso de Galton-Watson.)
Gap universality of generalized Wigner and -ensembles
We consider generalized Wigner ensembles and general -ensembles with analytic potentials for any . The recent universality results in particular assert that the local averages of consecutive eigenvalue gaps in the bulk of the spectrum are universal in the sense that they coincide with those of the corresponding Gaussian -ensembles. In this article, we show that local averaging is not necessary for this result, i.e. we prove that the single gap distributions in the bulk are universal. In fact,...
G-convergence of generators and weak convergence of diffusions
Genealogies of regular exchangeable coalescents with applications to sampling
This article considers a model of genealogy corresponding to a regular exchangeable coalescent (also known as -coalescent) started from a large finite configuration, and undergoing neutral mutations. Asymptotic expressions for the number of active lineages were obtained by the author in a previous work. Analogous results for the number of active mutation-free lineages and the combined lineage lengths are derived using the same martingale-based technique. They are given in terms of convergence in...
Genealogy of flows of continuous-state branching processes via flows of partitions and the Eve property
We encode the genealogy of a continuous-state branching process associated with a branching mechanism – or in short – using a stochastic flow of partitions. This encoding holds for all branching mechanisms and appears as a very tractable object to deal with asymptotic behaviours and convergences. In particular we study the so-called Eve property – the existence of an ancestor from which the entire population descends asymptotically – and give a necessary and sufficient condition on the for...
General approximation method for the distribution of Markov processes conditioned not to be killed
We consider a strong Markov process with killing and prove an approximation method for the distribution of the process conditioned not to be killed when it is observed. The method is based on a Fleming−Viot type particle system with rebirths, whose particles evolve as independent copies of the original strong Markov process and jump onto each others instead of being killed. Our only assumption is that the number of rebirths of the Fleming−Viot type system doesn’t explode in finite time almost surely...
General branching processes conditioned on extinction are still branching processes.
General Purpose Model of Queue Dissipation Time at Service Facility with Intermittent Bulk Service Schedule
General state space Markov chains and MCMC algorithms.
Generalised transforms, quasi-diffusions, and Désiré André's equation
Generalized Bessel function of type .
Generalized Cauchy identities, trees and multidimensional Brownian motions. I: Bijective proof of generalized Cauchy identities.
Generators of Brownian motions on abstract Wiener spaces
We prove that Brownian motion on an abstract Wiener space B generates a locally equicontinuous semigroup on equipped with the -topology introduced by L. Le Cam. Hence we obtain a “Laplace operator” as its infinitesimal generator. Using this Laplacian, we discuss Poisson’s equation and heat equation, and study its properties, especially the difference from the Gross Laplacian.
Generic Properties of Continuous Iterated Function Systems with Place Dependent Probabilities
It is shown that for a typical continuous learning system defined on a compact convex subset of ℝⁿ the Hausdorff dimension of its invariant measure is equal to zero.
Generic properties of iterated function systems with place dependent probabilities.
Generic properties of learning systems
It is shown that the set of learning systems having a singular stationary distribution is generic in the family of all systems satisfying the average contractivity condition.
Geodesics and crossing brownian motion in a soft poissonian potential
Geometric ergodicity and hybrid Markov chains.
Geometric ergodicity and perfect simulation.
Geometric evolution under isotropic stochastic flow.