Related papers: The Second Phase Transition of the Contact Process…
Recently, De Martino et al have presented a general framework for the study of transportation phenomena on complex networks. One of their most significant achievements was a deeper understanding of the phase transition from the uncongested…
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…
Random spanning trees are among the most prominent determinantal point processes. We give four examples of random spanning trees on ladder-like graphs whose rungs form stationary renewal processes or regenerative processes of order two,…
Using Monte Carlo model of biological evolution we have discovered that populations can switch between two different strategies of their genomes' evolution; Darwinian purifying selection and complementing the haplotypes. The first one is…
In epidemiological modelling, dynamics on networks, and in particular adaptive and heterogeneous networks have recently received much interest. Here we present a detailed analysis of a previously proposed model that combines heterogeneity…
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…
This paper is centered on the random graph generated by a Doeblin-type coupling of discrete time processes on a countable state space whereby when two paths meet, they merge. This random graph is studied through a novel subgraph, called a…
A bootstrap percolation process on a graph $G$ is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least $r$ infected neighbours…
Let $\mathbb{S}_g$ be the orientable surface of genus $g$. We prove that the component structure of a graph chosen uniformly at random from the class $\mathcal{S}_g(n,m)$ of all graphs on vertex set $[n]=\{1,\dotsc,n\}$ with $m$ edges…
We present an explicit connected spanning structure that appears in a random graph just above the connectivity threshold with high probability.
We study the appearance of first-order dynamical phase transitions (DPTs) as `intermittent' co-existing phases in the fluctuations of random walks on graphs. We show that the diverging time scale leading to critical behaviour is the waiting…
An outstanding problem of interdisciplinary interest is to understand quantitatively the role of social contacts in contagion dynamics. In general, there are two types of contacts: close ones among friends, colleagues and family members,…
We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…
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…
Let $G$ be the product of finitely many trees $T_1\times T_2 \times \cdots \times T_N$, each of which is regular with degree at least three. We consider Bernoulli bond percolation and the Ising model on this graph, giving a short proof that…
We consider the ground-state properties of the s=1/2 Ising chain in a transverse field which varies regularly along the chain having a period of alternation 2. Such a model, similarly to its uniform counterpart, exhibits quantum phase…
We consider a specific random graph which serves as a disordered medium for a particle performing biased random walk. Take a two-sided infinite horizontal ladder and pick a random spanning tree with a certain edge weight $c$ for the…
We consider bootstrap percolation on uncorrelated complex networks. We obtain the phase diagram for this process with respect to two parameters: $f$, the fraction of vertices initially activated, and $p$, the fraction of undamaged vertices…
The generic feature of traffic in a network of flowing electronic data packets is a phase transition from a stationary free-flow phase to a continuously growing congested non-stationary phase. In the most simple network of directed oriented…
We introduce two simple two-dimensional lattice models to study traffic flow in cities. We have found that a few basic elements give rise to the characteristic phase diagram of a first-order phase transition from a freely moving phase to a…