Related papers: Competing first passage percolation on random regu…
The theorem of Dekking and Host regarding tightness around the mean of first passage percolation on the binary tree, from the root to a boundary of a ball, is generalized to a class of graphs which includes all lattices in hyperbolic spaces…
The theme of this paper is the analysis of bootstrap percolation processes on random graphs generated by preferential attachment. This is a class of infection processes where vertices have two states: they are either infected or…
This article introduces a model for interacting vertex-reinforced random walks, each taking values on a complete sub-graph of a locally finite undirected graph. The transition probability for a walk to a given vertex depends on the…
In this paper, we study the competition of two diffusion processes for achieving the maximum possible diffusion in an area. This competition, however, does not occur in the same circumstance; one of these processes is a normal diffusion…
We deal with a random graph model where at each step, a vertex is chosen uniformly at random, and it is either duplicated or its edges are deleted. Duplication has a given probability. We analyse the limit distribution of the degree of a…
Human to human transmissible infectious diseases spread in a population using human interactions as its transmission vector. The early stages of such an outbreak can be modeled by a graph whose edges encode these interactions between…
When a new product enters a market already dominated by an existing product, will it survive along with this dominant product? Most of the existing works have shown the coexistence of two competing products spreading/being adopted on…
The main contribution of this paper is the development of a novel approach to multi-scale analysis that we believe can be used to analyse processes with non-equilibrium dynamics. Our approach will be referred to as \emph{multi-scale…
In this paper we study first-passage percolation in the configuration model with empirical degree distribution that follows a power-law with exponent $\tau \in (2,3)$. We assign independent and identically distributed (i.i.d.)\ weights to…
The dynamic behaviour of stochastic spreading processes on a network model based on k-regular graphs is investigated. The contact process and the susceptible-infected-susceptible model for the spread of epidemics are considered as prototype…
We investigate random walks on complex networks and derive an exact expression for the mean first passage time (MFPT) between two nodes. We introduce for each node the random walk centrality $C$, which is the ratio between its coordination…
Consider the following iterated process on a hypergraph $H$. Each vertex $v$ has an initial vertex weight. At each step, we uniformly at random select an edge $F$ in $H$, and for each vertex $v$ in $F$ we replace the weight of $v$ by the…
We study competition on scale-free random graphs, where the degree distribution satisfies an asymptotic power-law with infinite variance. Our competition process is such that the two types attempt at occupying vertices incident to the…
We consider first passage percolation with i.i.d. weights on edges of the d-dimensional cubic lattice. Under the assumptions that a weight is equal to zero with probability smaller than the critical probability of bond percolation in the…
We study the spread of multi-competitive viruses over a (possibly) time-varying network of individuals accounting for the presence of shared infrastructure networks that further enables transmission of the virus. We establish a sufficient…
Begin continuous time random walks from every vertex of a graph and have particles coalesce when they collide. We use a duality relation with the voter model to prove the process is site recurrent on bounded degree graphs, and for…
We introduce and study a non-oriented first passage percolation model having a property of statistical invariance by time reversal. This model is defined in a graph having directed edges and the passage times associated with each set of…
Bootstrap percolation on a graph is a deterministic process that iteratively enlarges a set of occupied sites by adjoining points with at least $\theta$ occupied neighbors. The initially occupied set is random, given by a uniform product…
We study the propagation of information in social networks. To do so, we focus on a cascade model where nodes are infected with {probability $p_1$ after their first contact with the information and with probability $p_2$ at all subsequent…
Given a two-dimensional correlated diffusion process, we determine the joint density of the first passage times of the process to some constant boundaries. This quantity depends on the joint density of the first passage time of the first…