Cadenas de Markov en poblaciones aleatorias y probabilidades en cadena generalizadas.
Changing the branching mechanism of a continuous state branching process using immigration
We consider an initial population whose size evolves according to a continuous state branching process. Then we add to this process an immigration (with the same branching mechanism as the initial population), in such a way that the immigration rate is proportional to the whole population size. We prove this continuous state branching process with immigration proportional to its own size is itself a continuous state branching process. By considering the immigration as the apparition of a new type,...
Collisions of random walks
A recurrent graph has the infinite collision property if two independent random walks on , started at the same point, collide infinitely often a.s. We give a simple criterion in terms of Green functions for a graph to have this property, and use it to prove that a critical Galton–Watson tree with finite variance conditioned to survive, the incipient infinite cluster in with and the uniform spanning tree in all have the infinite collision property. For power-law combs and spherically symmetric...
Competing species superprocesses with infinite variance.
Conditional limit theorems for branching processes.
Conditional limit theorems for intermediately subcritical branching processes in random environment
For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. For the subcritical regime a kind of phase transition appears. In this paper we study the intermediately subcritical case, which constitutes the borderline within this phase transition. We study the asymptotic behavior of the survival probability. Next the size of the population and the shape of the random environment...
Conditional processes induced by birth and death processes.
Conditioned brownian trees
Consistent minimal displacement of branching random walks.
Continuity of the percolation threshold in randomly grown graphs.
Continuous-time multitype branching processes conditioned on very late extinction
Multitype branching processes and Feller diffusion processes are conditioned on very late extinction. The conditioned laws are expressed as Doob h-transforms of the unconditioned laws, and an interpretation of the conditioned paths for the branching process is given, via the immortal particle. We study different limits for the conditioned process (increasing delay of extinction, long-time behavior, scaling limit) and provide an exhaustive list of exchangeability results.
Continuous-time multitype branching processes conditioned on very late extinction***
Multitype branching processes and Feller diffusion processes are conditioned on very late extinction. The conditioned laws are expressed as Doob h-transforms of the unconditioned laws, and an interpretation of the conditioned paths for the branching process is given, via the immortal particle. We study different limits for the conditioned process (increasing delay of extinction, long-time behavior, scaling limit) and provide an exhaustive list of exchangeability results.
Convergence of a “Gibbs-Boltzmann” random measure for a typed branching diffusion
Convergence of simple random walks on random discrete trees to brownian motion on the continuum random tree
In this article it is shown that the brownian motion on the continuum random tree is the scaling limit of the simple random walks on any family of discrete n-vertex ordered graph trees whose search-depth functions converge to the brownian excursion as n→∞. We prove both a quenched version (for typical realisations of the trees) and an annealed version (averaged over all realisations of the trees) of our main result. The assumptions of the article cover the important example of simple random walks...
Convex entropy decay via the Bochner–Bakry–Emery approach
We develop a method, based on a Bochner-type identity, to obtain estimates on the exponential rate of decay of the relative entropy from equilibrium of Markov processes in discrete settings. When this method applies the relative entropy decays in a convex way. The method is shown to be rather powerful when applied to a class of birth and death processes. We then consider other examples, including inhomogeneous zero-range processes and Bernoulli–Laplace models. For these two models, known results...
Correction : “Processus de Galton-Watson”
Critical branching diffusions : proper normalization and conditioned limit