Related papers: Percolation Threshold Results on \Erdos-\Renyi Gra…
Correlation analysis is a fundamental problem in statistics. In this paper, we consider the correlation detection problem between a pair of Erdos-Renyi graphs. Specifically, the problem is formulated as a hypothesis testing problem: under…
Methods for determining the percolation threshold usually study the behavior of network ensembles and are often restricted to a particular type of probabilistic node/link removal strategy. We propose a network-specific method to determine…
We study the two most common types of percolation process on a sparse random graph with a given degree sequence. Namely, we examine first a bond percolation process where the edges of the graph are retained with probability p and afterwards…
We consider certain respondent-driven sampling procedures on dense graphs. We show that if the sequence of the vertex-sets is ergodic then the limiting graph can be expressed in terms of the original dense graph via a transformation related…
Many complex networks in nature have directed links, a property that affects the network's navigability and large-scale topology. Here we study the percolation properties of such directed scale-free networks with correlated in- and…
We obtain new lower bounds on the critical points for various models of oriented percolation. The method is to provide a stochastic domination of the percolation processes by multitype Galton-Watson trees. This can be apply to the classical…
We locate the critical threshold $p_c$ at which it becomes likely that the complete graph $K_n$ can be obtained from the Erd\H{o}s-R\'enyi graph ${\cal G}_{n,p}$ by iteratively completing copies of $K_4$ minus an edge. This refines work of…
We study directed percolation at the upper critical transverse dimension $d=4$, where critical fluctuations induce logarithmic corrections to the leading (mean-field) behavior. Viewing directed percolation as a kinetic process, we address…
Percolation is a concept widely used in many fields of research and refers to the propagation of substances through porous media (e.g., coffee filtering), or the behaviour of complex networks (e.g., spreading of diseases). Percolation…
The present work introduces an efficient Monte Carlo algorithm for continuum percolation composed of randomly-oriented rectangles. By conducting extensive simulations, we report high precision percolation thresholds for a variety of…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
Jigsaw percolation is a model for the process of solving puzzles within a social network, which was recently proposed by Brummitt, Chatterjee, Dey and Sivakoff. In the model there are two graphs on a single vertex set (the `people' graph…
We study low-Reynolds-number fluid flow through a two-dimensional porous medium modeled as a Lorentz gas. Using extensive finite element simulations we fully resolve the flow fields for packing fractions approaching the percolation…
The location and nature of the percolation transition in random networks is a subject of intense interest. Recently, a series of graph evolution processes have been introduced that lead to discontinuous percolation transitions where the…
Erdos-Renyi limit laws give the length scale of a time-window over which time-averages in Birkhoff sums have a non-trivial almost-sure limit. We establish Erdos-Renyi type limit laws for Holder observables on dynamical systems modeled by…
We consider random walks on random graphs, focusing on return probabilities and hitting times for sparse Erdos-Renyi graphs. Using the tree approach which is expected to be exact in the large graph limit, we show how to solve for the…
We consider directed random graphs, the prototype of which being the Barak-Erd\H{o}s graph $\vec G(\mathbb Z, p)$, and study the way that long (or heavy, if weights are present) paths grow. This is done by relating the graphs to certain…
We consider a directed variant of the negative-weight percolation model in a two-dimensional, periodic, square lattice. The problem exhibits edge weights which are taken from a distribution that allows for both positive and negative values.…
A graph $G$ percolates in the $K_{r,s}$-bootstrap process if we can add all missing edges of $G$ in some order such that each edge creates a new copy of $K_{r,s}$, where $K_{r,s}$ is the complete bipartite graph. We study…
Majority bootstrap percolation on a graph $G$ is an epidemic process defined in the following manner. Firstly, an initially infected set of vertices is selected. Then step by step the vertices that have more infected than non-infected…