Related papers: Renewal Contact Processes: phase transition and su…
We study the contact process on the complete graph on $n$ vertices where the rate at which the infection travels along the edge connecting vertices $i$ and $j$ is equal to $ \lambda w_i w_j / n$ for some $\lambda >0$, where $w_i$ are i.i.d.…
Many-variable differential equations with random coefficients provide powerful models for the dynamics of many interacting species in ecology. These models are known to exhibit a dynamical phase transition from a phase where population…
We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and…
We present and establish large deviations principles for general multivariate renewal-reward processes associated with a classical discrete-time renewal process. A renewal-reward process describes a cumulative reward over time, supposing…
Let $(\xi_k,\eta_k)_{k\in\mathbb{N}}$ be independent identically distributed random vectors with arbitrarily dependent positive components. We call a (globally) perturbed random walk a random sequence $T:=(T_k)_{k\in\mathbb{N}}$ defined by…
The contact process is a particular case of birth-and-death processes on infinite particle configurations. We consider the contact models on locally compact separable metric spaces. We prove the existence of a one-parameter set of invariant…
We consider quasi-stationary distributions for one-dimensional diffusions via the renewal dynamical approach. We show that convergence of the iterative renewal transform to quasi-stationary distributions is equivalent to a condition on the…
The enhancement of pions and kaons observed at small transverse momenta in ultra-relativistic heavy-ion collisions may at least partly reflect critical scattering expected to occur in the neighborhood of a second order phase transition.…
We establish global convergence of the (1+1) evolution strategy, i.e., convergence to a critical point independent of the initial state. More precisely, we show the existence of a critical limit point, using a suitable extension of the…
Renewal theory is finding increasing applications in non-equilibrium statistical physics. One example relates the probability density and survival probability of a Brownian particle or an active run-and-tumble particle with stochastic…
By introducing the notions of living and dead nodes a new model of random tree evolution with continuous time parameter has been constructed. It is assumed that two random variables, the lifetime and the offspring number of living nodes…
We prove that the supercritical one-dimensional contact process survives in certain wedge-like space-time regions, and that when it survives it couples with the unrestricted contact process started from its upper invariant measure. As an…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
Renewal processes with heavy-tailed power law distributed sojourn times are commonly encountered in physical modelling and so typical fluctuations of observables of interest have been investigated in detail. To describe rare events the rate…
We consider an interacting particle system on $\Z^d$ with finite state space and interactions of infinite range in a high-noise regime. Assuming that the rate of change is continuous and that a Dobrushin-like condition holds, we show that…
We investigate the contact process on four different types of scale-free inhomogeneous random graphs evolving according to a stationary dynamics, where each potential edge is updated with a rate depending on the strength of the adjacent…
Renewal process is a point process where an inter-event time between successive renewals is an independent and identically distributed random variable. Alternating renewal process is a dichotomous process and a slight generalization of the…
We prove exponential decay of pair correlations for 1D stationary point processes when spacings satisfy a Markov condition, geometric ergodicity, and a condition on exponential moments. The conditions are phrased for stationary sequences of…
We study the threshold $\theta$ contact process on $\mathbb{Z}^d$ with infection parameter $\lambda$. We show that the critical point $\lambda_{\mathrm{c}}$, defined as the threshold for survival starting from every site occupied, vanishes…
We consider shot noise processes $(X(t))_{t \geq 0}$ with deterministic response function $h$ and the shots occurring at the renewal epochs $0= S_0 < S_1 < S_2 ...$ of a zero-delayed renewal process. We prove convergence of the…