Related papers: Renewal contact process with dormancy
We study the contact process in a dynamical random environment defined on the vertices and edges of a graph. For a broad class of processes, we establish an asymptotic shape theorem for the set H_t, which represents the vertices that have…
We show results for the contact process on Barabasi networks. The contact process is a model for an epidemic spreading without permanent immunity that has an absorbing state. For finite lattices, the absorbing state is the true stationary…
Motivated by the wide range of known self-replicating systems, some far from genetics, we study a system composed by individuals having an internal dynamics with many possible states that are partially stable, with varying mutation rates.…
We study survival and extinction of a long-range infection process on a diluted one-dimensional lattice in discrete time. The infection can spread to distant vertices according to a Pareto distribution, however spreading is also prohibited…
We investigate the interplay between two fundamental mechanisms of microbial population dynamics and evolution called dormancy and horizontal gene transfer. The corresponding traits come in many guises and are ubiquitous in microbial…
Given a weighted graph, we introduce a partition of its vertex set such that the distance between any two clusters is bounded from below by a power of the minimum weight of both clusters. This partition is obtained by recursively merging…
We consider a renewal-reward process with multivariate rewards. Such a process is constructed from an i.i.d.\ sequence of time periods, to each of which there is associated a multivariate reward vector. The rewards in each time period may…
We consider random variables observed at arrival times of a renewal process, which possibly depends on those observations and has regularly varying steps with infinite mean. Due to the dependence and heavy tailed steps, the limiting…
The stacked contact process is a three-state spin system that describes the co-evolution of a population of hosts together with their symbionts. In a nutshell, the hosts evolve according to a contact process while the symbionts evolve…
We study the effects of switching social contacts as a strategy to control epidemic outbreaks. Connections between susceptible and infective individuals can be broken by either individual, and then reconnected to a randomly chosen member of…
The cell cycle duration is a variable cellular phenotype that underlies long-term population growth and age structures. By analyzing the stationary solutions of a branching process with heritable cell division times, we demonstrate…
An asymmetric variant of the contact process where the activity spreads with different and independent random rates to the left and to the right is introduced. A real space renormalization scheme is formulated for model by means of which it…
Aging refers to the property of two-time correlation functions to decay very slowly on (at least) two time scales. This phenomenon has gained recent attention due to experimental observations of the history dependent relaxation behavior in…
We consider a renewal process with regularly varying stationary and weakly dependent steps, and prove that the steps made before a given time $t$, satisfy an interesting invariance principle. Namely, together with the age of the renewal…
The interaction between individuals in biological populations, dilute components of chemical systems, or particles transported by turbulent flows depends critically on their contact statistics. This work clarifies those statistics under the…
We continue the study of renewal contact processes initiated in a companion paper, where we showed that if the tail of the interarrival distribution $\mu$ is heavier than $t^{-\alpha}$ for some $\alpha <1$ (plus auxiliary regularity…
We study a simple random process in which vertices of a connected graph reach consensus through pairwise interactions. We compute outcome probabilities, which do not depend on the graph structure, and consider the expected time until a…
The electrical resistance decay of a metallic granular packing has been measured as a function of time. This measurement gives information about the size of the conducting cluster formed by the well connected grains. Several regimes have…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
Prior social contagion models consider the spread of either one contagion at a time on interdependent networks or multiple contagions on single layer networks or under assumptions of competition. We propose a new threshold model for the…