Related papers: Infinite rate mutually catalytic branching

We study the phenomenon of coming down from infinity - that is, when the process starts from infinity and never returns to it - for continuous-state branching processes with generalized drift. We provide sufficient conditions on the drift…

We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…

We consider inhomogeneous branching diffusions on an infinite domain of $\mathbb{R}^d$. The first aim of this article is to derive a general criterium under which the size process (number of particles) and the genealogy of the particle…

We derive a self-duality relation for a one-dimensional model of branching and annihilating random walkers with an even number of offsprings. With the duality relation and by deriving exact results in some limiting cases involving fast…

We give an example of a long range Bernoulli percolation process on a group non-quasi-isometric with $\mathbb{Z}$, in which clusters are almost surely finite for all values of the parameter. This random graph admits diverse equivalent…

In this article we contribute to the moment analysis of branching processes in catalytic media. The many-to-few lemma based on the spine technique is used to derive a system of (discrete space) partial differential equations for the number…

We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…

In this thesis, we study asymptotic properties of the standard branching Brownian motion, with a specific emphasis on the additive martingales at high temperature. We start by presenting classic and fundamental tools for our investigation.…

An infinite system of point particles placed in $\mathds{R}^d$ is studied. Its constituents perform random jumps with mutual repulsion described by a translation-invariant jump kernel and interaction potential, respectively. The pure states…

We introduce polynomial processes taking values in an arbitrary Banach space $B$ via their infinitesimal generator $L$ and the associated martingale problem. We obtain two representations of the (conditional) moments in terms of solutions…

We study the long time behaviour of a Markov process evolving in $\mathbb{N}$ and conditioned not to hit 0. Assuming that the process comes back quickly from infinity, we prove that the process admits a unique quasi-stationary distribution…

We show that a large class of stationary continuous-time regenerative processes are finitarily isomorphic to one another. The key is showing that any stationary renewal point process whose jump distribution is absolutely continuous with…

For a supercritical catalytic branching random walk on Z^d (d is positive integer) with an arbitrary finite catalysts set we study the spread of particles population as time grows to infinity. Namely, we divide by t the position coordinates…

We define and study fractional versions of the well-known Gamma subordinator $\Gamma :=\{\Gamma (t),$ $t\geq 0\},$ which are obtained by time-changing $% \Gamma $ by means of an independent stable subordinator or its inverse. Their…

We study fermions that are gauge-coupled to a cavity mode via Raman-assisted hopping in a one dimensional lattice. For an infinite lattice, we find a superradiant phase with infinitesimal pumping threshold which induces a directed particle…

We study a critical multitype Bellman--Harris branching particle system in \(\mathbb R^N\) with a finite type space \(\mathbf K=\{1,\dots,K\}\). Particles of type \(I\) move according to a symmetric \(\alpha_i\)-stable process, have…

We investigate entanglement dynamics in multipartite systems, establishing a quantitative concept of entanglement flow: both flow through individual particles, and flow along general networks of interacting particles. In the former case,…

Conditioning a multitype Galton-Watson process to stay alive into the indefinite future leads to what is known as its associated $Q$-process. We show that the same holds true if the process is conditioned to reach a positive threshold or a…

Let ${Z_{n},n\geq 0} $ be a critical branching process in random environment and let $T$ be its moment of extinction. Under the annealed approach we prove, as $n\to \infty ,$ a limit theorem for the number of particles in the process at…

We study positive random variables whose moments can be expressed by products and quotients of Gamma functions; this includes many standard distributions. General results are given on existence, series expansion and asymptotics of density…