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We consider random networks whose dynamics is described by a rate equation, with transition rates $w_{nm}$ that form a symmetric matrix. The long time evolution of the system is characterized by a diffusion coefficient $D$. In one dimension…
A simple one-dimensional microscopic model of the depinning transition of an interface from an attractive hard wall is introduced and investigated. Upon varying a control parameter, the critical behaviour observed along the transition line…
Based on numerical simulation and local stability analysis we describe the structure of the phase space of the edge/triangle model of random graphs. We support simulation evidence with mathematical proof of continuity and discontinuity for…
It is a common practice to describe branching random walks in terms of birth, death and walk of particles, which makes it easier to use them in different applications. The main results obtained for the models of symmetric continuous-time…
We develop a probabilistic framework for global modeling of the traffic over a computer network. This model integrates existing single-link (-flow) traffic models with the routing over the network to capture the global traffic behavior. It…
We consider a one-dimensional network in which the nodes at Euclidean distance $l$ can have long range connections with a probabilty $P(l) \sim l^{-\delta}$ in addition to nearest neighbour connections. This system has been shown to exhibit…
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…
We consider the wetting transition in the framework of an effective interface model of gradient type, in dimension 2 and higher. We prove pathwise estimates showing that the interface is localized in the whole thermodynamically-defined…
A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition…
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…
Most car-following models show a transition from laminar to ``congested'' flow and vice versa. Deterministic models often have a density range where a disturbance needs a sufficiently large critical amplitude to move the flow from the…
We consider the random deposition of objects of variable width and height over a line. The successive additions of these structures create a random interface. We focus on the regime of heavy tailed distributions of the structure width. When…
Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…
The study of dynamical large deviations allows for a characterization of stationary states of lattice gas models out of equilibrium conditioned on averages of dynamical observables. The application of this framework to the two-dimensional…
We study a random matrix model for the statistical properties of the purity of a bipartite quantum system at a finite (fictitious) temperature. This enables us to write the generating function for the cumulants, for both balanced and…
Predicting the future behaviour of complex systems exhibiting critical-like dynamics is often considered to be an intrinsically hard task. Here, we study the predictability of the depinning dynamics of elastic interfaces in random media…
Linear max-plus systems describe the behavior of a large variety of complex systems. It is known that these systems show a periodic behavior after an initial transient phase. Assessment of the length of this transient phase provides…
We propose experimentally feasible ways to probe universal features of absorbing phase transitions from two different approaches, both based on numerical validations. On one hand, we numerically study a probability distribution of…
This paper investigates properties of the class of graphs based on exchangeable point processes. We provide asymptotic expressions for the number of edges, number of nodes and degree distributions, identifying four regimes: (i) a dense…
Social fragmentation transition is a transition of social states between many disconnected communities with distinct opinions and a well-connected single network with homogeneous opinions. This is a timely research topic with high relevance…