Related papers: Metastability for the contact process on the prefe…

We consider contact processes on the hierarchical group, where sites infect other sites at a rate depending on their hierarchical distance, and sites become healthy with a constant recovery rate. If the infection rates decay too fast as a…

In this paper we investigate geometric properties of graphs generated by a preferential attachment random graph model with edge-steps. More precisely, at each time $t\in\mathbb{N}$, with probability $p$ a new vertex is added to the graph (a…

It is known that the limiting behavior of the contact process strongly depends upon the geometry of the graph on which particles evolve: while the contact process on the regular lattice exhibits only two phases, the process on homogeneous…

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…

In this paper, we derive a precise estimate for the mean extinction time of the contact process with a fixed infection rate on a star graph with $N$ leaves. Specifically, we determine not only the exponential main factor but also the exact…

For a sequence of random graphs, the limit law we refer to is the existence of a limiting probability of any graph property that can be expressed in terms of predicate logic. A zero-one limit law is shown by Shelah and Spencer for…

Propagation of contagion in networks depends on the graph topology. This paper is concerned with studying the time-asymptotic behavior of the extended contact processes on static, undirected, finite-size networks. This is a contact process…

In this paper we will consider the contact process in a very simple type of random environment that physicists call the random dilution model. We start with the contact process on a graph, here either $\mathbb{Z}^d$, a $d$-dimensional torus…

We propose a model of network formation based on reinforcement learning, which can be seen as a generalization as the one proposed by Skyrms for signaling games. On a discrete graph, whose vertices represent individuals, at any time step…

We study the behavior of algebraic connectivity in a weighted graph that is subject to site percolation, random deletion of the vertices. Using a refined concentration inequality for random matrices we show in our main theorem that the…

We study majority dynamics on the binomial random graph $G(n,p)$ with $p = d/n$ and $d > \lambda n^{1/2}$, for some large $\lambda>0$. In this process, each vertex has a state in $\{-1,+1 \}$ and at each round every vertex adopts the state…

The contact process on dynamic edges (CPDE) is a contact process evolving on a dynamic environment given by a dynamical percolation on the edges of Z d\,: each edge updates its state to open or closed with respective rates vp and v(1 -p).…

We study degree-penalized contact processes on Galton-Watson trees (GW) and the configuration model. The model we consider is a modification of the usual contact process on a graph. In particular, each vertex can be either infected or…

The asymptotic shape theorem for the contact process in random environment gives the existence of a norm $\mu$ on $\Rd$ such that the hitting time $t(x)$ is asymptotically equivalent to $\mu(x)$ when the contact process survives. We provide…

We establish two open problems from Kesten and Sidoravicius [8]. Particles are initially placed on $\Z^{d}$ with a given density and evolve as independent continuous-time random walks. Particles initially placed at the origin are declared…

We study the evolution of the graph distance and weighted distance between two fixed vertices in dynamically growing random graph models. More precisely, we consider preferential attachment models with power-law exponent $\tau\in(2,3)$,…

In this paper we are concerned with the contact process with semi-infected state on the complete graph $C_n$ with $n$ vertices. In our model, each vertex is in one of three states that `healthy', `semi-infected' or `wholly-infected'. Only…

Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple…

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…

In a highly influential paper twenty years ago, Barab\'asi and Albert [Science 286, 509 (1999)] showed that networks undergoing generic growth processes with preferential attachment evolve towards scale-free structures. In any finite…