Related papers: Contact process on one-dimensional long-range perc…
In this article, we study a bond percolation model on a horizontally stretched square lattice, constructed by stretching the distances between the columns of $\mathbb{Z}_+^2$ according to a collection of independent and identically…
The pressure-temperature phase diagram of a one-component system, with particles interacting through a spherically symmetric pair potential is studied. It is shown that if the pair potential allows for a discontinuous reduction of the…
Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase transitions were believed to be continuous until recently…
Hypergraphs capture the higher-order interactions in complex systems and always admit a factor graph representation, consisting of a bipartite network of nodes and hyperedges. As hypegraphs are ubiquitous, investigating hypergraph…
In this paper, we prove that Bernoulli percolation on bounded degree graphs with isoperimetric dimension $d>4$ undergoes a non-trivial phase transition (in the sense that $p_c<1$). As a corollary, we obtain that the critical point of…
We study versions of the contact process with three states, and with infections occurring at a rate depending on the overall infection density. Motivated by a model described in [17] for vegetation patterns in arid landscapes, we focus on…
The `random intersection graph with communities' models networks with communities, assuming an underlying bipartite structure of groups and individuals. Each group has its own internal structure described by a (small) graph, while groups…
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…
A generalized zero-range process with a limited number of long-range interactions is studied as an example of a transport process in which particles at a T-junction make a choice of which branch to take based on traffic levels on each…
We consider self-avoiding walk and percolation in $\Zd$, oriented percolation in $\Zd\times\Zp$, and the contact process in $\Zd$, with $p D(\cdot)$ being the coupling function whose range is denoted by $L<\infty$. For percolation, for…
It is known that many different types of finite random subgraph models undergo quantitatively similar phase transitions around their percolation thresholds, and the proofs of these results rely on isoperimetric properties of the underlying…
This paper is devoted to the study of particular geometrically defined intersection classes of graphs. Those were previously studied by Magnant and Martin, who proved that these graphs have arbitrary large chromatic number, while being…
The dynamical properties of a dense horizontally vibrated bidisperse granular monolayer are experimentally investigated. The quench protocol produces states with a frozen structure of the assembly, but the remaining degrees of freedom…
A useful result about leftmost and rightmost paths in two dimensional bond percolation is proved. This result was introduced without proof in \cite{G} in the context of the contact process in continuous time. As discussed here, it also…
We consider a generalization of the contact process stochastic model, including an additional autocatalitic process. The phase diagram of this model in the proper two-parameter space displays a line of transitions between an active and an…
A method is introduced whereby two non-interacting quantum subsystems, that each interact with a third subsystem, are entangled via repeated projective measurements of the state of the third subsystem. A variety of physical examples are…
We consider near-critical planar systems with boundary conditions inducing phase separation. While order parameter correlations decay exponentially in pure phases, we show by direct field theoretical derivation how phase separation…
In the multitype contact process, vertices of a graph can be empty or occupied by a type 1 or a type 2 individual; an individual of type $i$ dies with rate 1 and sends a descendant to a neighboring empty site with rate $\lambda_i$. We study…
It is known that diffusion provokes substantial changes in continuous absorbing phase transitions. Conversely, its effect on discontinuous transitions is much less understood. In order to shed light in this direction, we study the inclusion…
A necessary and sufficient condition is established for the strict inequality $p_c(G_*)<p_c(G)$ between the critical probabilities of site percolation on a quasi-transitive, plane graph $G$ and on its matching graph $G_*$. It is assumed…