Related papers: From transience to recurrence with Poisson tree fr…

Intransitivity is a property of connected, oriented graphs representing species interactions that may drive their coexistence even in the presence of competition, the standard example being the three species Rock-Paper-Scissors game. We…

It has been noticed that when the waiting time distribution exhibits a transition from an intermediate time power law decay to a long-time exponential decay in the continuous time random walk model, a transition from anomalous diffusion to…

We solve exactly a model of monodispersed rigid rods of length $k$ with repulsive interactions on the random locally tree like layered lattice. For $k\geq 4$ we show that with increasing density, the system undergoes two phase transitions:…

Motivated by experiments on sheared suspensions that show a transition between ordered and disordered phases, we here study the long-time behavior of a sheared and overdamped 2-d system of particles interacting by repulsive forces. As a…

Trees or rooted trees have been generously studied in the literature. A forest is a set of trees or rooted trees. Here we give recurrence relations between the number of some kind of rooted forest with $k$ roots and that with $k+1$ roots on…

We study a random fragmentation process and its associated random tree. The process has earlier been studied by Dean and Majumdar (J. Phys. A: Math. Gen., vol. 35, L501--L507), who found a phase transition: the number of fragmentations is…

We study the frog model on \( \mathbb{Z} \) with geometric lifetimes, introducing a random survival parameter. Active and inactive particles are placed at the vertices of \( \mathbb{Z} \). The lifetime of each active particle follows a…

We investigate a spatial random graph model whose vertices are given as a marked Poisson process on $\mathbb{R}^d$. Edges are inserted between any pair of points independently with probability depending on the spatial displacement of the…

We consider a branching random walk on $\Z$, where the particles behave differently in visited and unvisited sites. Informally, each site on the positive half-line contains initially a cookie. On the first visit of a site its cookie is…

We study the random transverse field Ising model on a finite Cayley tree. This enables us to probe key questions arising in other important disordered quantum systems, in particular the Anderson transition and the problem of dirty bosons on…

This paper introduces the Attracting Random Walks model, which describes the dynamics of a system of particles on a graph with $n$ vertices. At each step, a single particle moves to an adjacent vertex (or stays at the current one) with…

We study how the recurrence and transience of space-time sets for a branching random walk on a graph depends on the offspring distribution. Here, we say that a space-time set $A$ is recurrent if it is visited infinitely often almost surely…

We study a particle system with hopping (random walk) dynamics on the integer lattice $\mathbb Z^d$. The particles can exist in two states, active or inactive (sleeping); only the former can hop. The dynamics conserves the number of…

We study structural transitions in a system of interacting particles arranged as a crystalline bilayer, as a function of the density $\rho$ and the distance $d$ between the layers. As $d$ is decreased a sequence of transitions involving…

We study the role of noise on the nature of the transition to collective motion in dry active matter. Starting from field theories that predict a continuous transition at the deterministic level, we show that fluctuations induce a…

Cyclic predator-prey models with four or six species are studied on a square lattice when the invasion rates are varied. It is found that the cyclic invasions maintain a self-organizing pattern as long as the deviation of the invasion…

We study the intermittent fluorescence of a single molecule, jumping from the "light on" to the "light off" state, as a Poisson process modulated by a fluctuating environment. We show that the quasi-periodic and quasi-deterministic…

The main substance of the paper concerns the growth rate and the classification (ergodicity, transience) of a family of random trees. In the basic model, new edges appear according to a Poisson process of parameter $\lambda$ and leaves can…

Distinguishing between continuous and first-order phase transitions is a major challenge in random discrete systems. We study the topic for events with recursive structure on Galton-Watson trees. For example, let $\mathcal{T}_1$ be the…

We study the phase behaviour of a fluid composed of particles which interact via a pair potential that is repulsive for large inter-particle distances, is attractive at intermediate distances and is strongly repulsive at short distances…