Related papers: Continuous-state branching processes with competit…
We review the entanglement properties in collective models and their relationship with quantum phase transitions. Focusing on the concurrence which characterizes the two-spin entanglement, we show that for first-order transition, this…
We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process…
We consider a birth-death process with the birth rates $i\lambda$ and death rates $i\mu +i(i-1)\theta$, where $i$ is the current state of the process. A positive competition rate $\theta$ is assumed to be small. In the supercritical case…
The totally asymmetric simple exclusion process in discrete time is considered on finite rings with fixed number of particles. A translation-invariant version of the backward-ordered sequential update is defined for periodic boundary…
We study an extension of the so-called defective Galton-Watson processes obtained by allowing the offspring distribution to change over the generations. Thus, in these processes, the individuals reproduce independently of the others and in…
We consider the facilitated exclusion process, an interacting particle system on the integer line where particles hop to one of their left or right neighbouring site only when the other neighbouring site is occupied by a particle. A…
Subcritical catalytic branching random walk on d-dimensional lattice is studied. New theorems concerning the asymptotic behavior of distributions of local particles numbers are established. To prove the results different approaches are used…
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…
Network properties govern the rate and extent of various spreading processes, from simple contagions to complex cascades. Recently, the analysis of spreading processes has been extended from static networks to temporal networks, where nodes…
We study the gap processes in a degenerate system of three particles interacting through their ranks. We obtain the Laplace transform of the invariant measure of these gaps, and an explicit expression for the corresponding invariant…
The goal of this article is to contribute towards the conceptual and quantitative understanding of the evolutionary benefits for (microbial) populations to maintain a seed bank (consisting of dormant individuals) when facing fluctuating…
By considering the master equation of asymmetric exclusion process on a one-dimensional lattice, we obtain the most general boundary condition of the multi-species exclusion processes in which the number of particles is constant in time.…
Contact processes (CP's) with particle creation requiring a minimal neighborhood (restrictive or threshold CP's) present a novel sort of discontinuous absorbing transitions, that revealed itself robust under the inclusion of different…
According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which…
This paper provides an adaptation of branching bisimilarity to reactive systems with time-outs. Multiple equivalent definitions are procured, along with a modal characterisation and a proof of its congruence property for a standard process…
In this work we model the dynamics of a population that evolves as a continuous time branching process with a trait structure and ecological interactions in form of mutations and competition between individuals. We generalize existing…
The purpose of this paper is to investigate properties of self-exciting jump processes. We derive the Laplace transform of SDE driven self-exciting processes with independent, identically distributed jump sizes. By using this Laplace…
Zero-range processes with decreasing jump rates are known to exhibit condensation, where a finite fraction of all particles concentrates on a single lattice site when the total density exceeds a critical value. We study such a process on a…
We consider a branching stable process with positive jumps, i.e. a continuous-time branching process in which the particles evolve independently as stable L{\'e}vy processes with positive jumps. Assuming the branching mechanism is critical…
Let $\{Z_{m},m\geq 0\}$ be a critical branching process in random environment and $\{S_{m},m\geq 0\}$ be its associated random walk. Assuming that the increments distribution of the associated random walk belongs without centering to the…