Related papers: A probabilistic model for interfaces in a martensi…

We consider a degenerate partial differential equation arising in population dynamics, namely the porous medium equation with a bistable reaction term. We study its asymptotic behavior as a small parameter, related to the thickness of a…

We study the susceptibility, i.e., the mean size of the component containing a random vertex, in a general model of inhomogeneous random graphs. This is one of the fundamental quantities associated to (percolation) phase transitions; in…

We study a model for the spread of an infectious disease which incorporates spatial and temporal effects. The model is a delayed multi-type branching process in which types represent geographic regions while infected individuals reproduce…

We study numerically the roughening properties of an interface in a two-dimensional Ising model with either random bonds or random fields, which are representative of universality classes where disorder acts only on the interface or also…

Our general subject is the emergence of phases, and phase transitions, in large networks subjected to a few variable constraints. Our main result is the analysis, in the model using edge and triangle subdensities for constraints, of a sharp…

The traditional node percolation map of directed networks is reanalyzed in terms of edges. In the percolated phase, edges can mainly organize into five distinct giant connected components, interfaces bridging the communication of nodes in…

We study a random fragmentation process and its associated random tree. The process has earlier been studied by Dean and Majumdar (J. Phys. A: Math. Gen., vol. 35, L501--L507), who found a phase transition: the number of fragmentations is…

In this paper we study the component structure of random graphs with independence between the edges. Under mild assumptions, we determine whether there is a giant component, and find its asymptotic size when it exists. We assume that the…

We derive a message passing method for computing the spectra of locally tree-like networks and an approximation to it that allows us to compute closed-form expressions or fast numerical approximates for the spectral density of random graphs…

We study the localisation of lattice polymer models near a permeable interface in two dimensions. Localisation can arise due to an interaction between the polymer and the interface, and can be altered by a preference for the bulk solvent on…

We consider a family of directed exponential random graph models parametrized by edges and outward stars. Much of the important statistical content of such models is given by the normalization constant of the models, and in particular, an…

Lattice-based random walk models are widely used to study populations of migrating cells with motility bias and proliferation. Crowding is typically represented by volume exclusion, where each lattice site can be occupied by at most one…

Threshold models try to explain the consequences of social influence like the spread of fads and opinions. Along with models of epidemics, they constitute a major theoretical framework of social spreading processes. In threshold models on…

Phase transitions are the macroscopic manifestation of microscopic processes that drive a system towards a new state. The detailed evolution of these processes, particularly in abrupt phase transitions, are currently not fully understood.…

We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…

We introduce a random intersection graph process aimed at modeling sparse evolving affiliation networks that admit tunable (power law) degree distribution and assortativity and clustering coefficients. We show the asymptotic degree…

An exactly solvable model for the rewiring dynamics of weighted, directed networks is introduced. Simulations indicate that the model exhibits two types of condensation: (i) a phase in which, for each node, a finite fraction of its total…

In this work we approach cell migration under a large-scale assumption, so that the system reduces to a particle in motion. Unlike classical particle models, the cell displacement results from its internal activity: the cell velocity is a…

Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…

With the advance of experimental techniques such as time-lapse fluorescence microscopy, the availability of single-cell trajectory data has vastly increased, and so has the demand for computational methods suitable for parameter inference…