Related papers: Frog model on $\mathbb{Z}$ with random survival pa…

We study the transition probability, say $p_A^n(x,y)$, of a one-dimensional random walk on the integer lattice killed when entering into a non-empty finite set $A$. The random walk is assumed to be irreducible and have zero mean and a…

We consider the dynamical evolution of a Brownian particle undergoing stochastic resetting, meaning that after random periods of time it is forced to return to the starting position. The intervals after which the random motion is stopped…

Random walks are powerful tools to analyze spatial-temporal patterns produced by living organisms ranging from cells to humans. At the same time, it is evident that these patterns are not completely random but are results of a convolution…

With a view to connecting random mutation on the molecular level to punctuated equilibrium behavior on the phenotype level, we propose a new model for biological evolution, which incorporates random mutation and natural selection. In this…

We study the variations of the principal eigenvalue associated to a growth-fragmentation-death equation with respect to a parameter acting on growth and fragmentation. To this aim, we use the probabilistic individual-based interpretation of…

We introduce random walks in a sparse random environment on $\mathbb Z$ and investigate basic asymptotic properties of this model, such as recurrence-transience, asymptotic speed, and limit theorems in both the transient and recurrent…

We present novel analytical results about ecosystem species diversity that stem from a proposed coarse grained neutral model based on birth-death processes. The relevance of the problem lies in the urgency for understanding and synthesizing…

We consider a quantum particle, moving on a lattice with a tight-binding Hamiltonian, which is subjected to measurements to detect it's arrival at a particular chosen set of sites. The projective measurements are made at regular time…

We consider a branching-selection particle system on the real line. In this model the total size of the population at time $n$ is limited by $\exp\left(a n^{1/3}\right)$. At each step $n$, every individual dies while reproducing…

In this paper, we introduce a nonresident computer virus model and prove the existence of at least one positive periodic solution. The proposed model is based on a biological approach and is obtained by considering that all rates (rates…

For many diseases it is reasonable to assume that the hazard rate is not constant across time, but also that it changes in different time intervals. To capture this, we work here with a piecewise survival model. One of the major problems in…

We consider a stochastic model of infection spread on the complete graph on $N$ vertices incorporating dynamic partnerships, which we assume to be monogamous. This can be seen as a variation on the contact process in which some form of edge…

In this paper we consider an irreducible random walk on the integer lattice $\mathbb{Z}$ that is in the domain of normal attraction of a strictly stable process with index $\alpha\in (1, 2)$ and obtain the asymptotic form of the…

Exploration and trapping properties of random walkers that may evanesce at any time as they walk have seen very little treatment in the literature, and yet a finite lifetime is a frequent occurrence, and its effects on a number of random…

We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random…

We argue that the dynamics of particle imbalance in quadratic fermionic models is, for the majority of initial many-body product states in site occupation basis, virtually indistinguishable from the dynamics of survival probabilities of…

We study the survival probability of an immobile target in presence of N independent diffusing walkers. We address the problem of the Mean Target Lifetime and its dependence on the number and initial distribution of the walkers when the…

We analyze the dynamics of the Sisyphus random walk model, a discrete Markov chain in which the walkers may randomly return to their initial position $x_0$. In particular, we present a remarkably compact derivation of the time-dependent…

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…

The extreme value statistics of active matter offer significant insight into their unique properties. A phase transition has recently been reported in a model of branching run-and-tumble particles, describing the spatial spreading of an…