Related papers: Analytical results on the polymerisation random gr…

Many research fields, reaching from social networks and epidemiology to biology and physics, have experienced great advance from recent developments in random graphs and network theory. In this paper we propose to view percolation on a…

We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random…

The polymer model framework is a classical tool from statistical mechanics that has recently been used to obtain approximation algorithms for spin systems on classes of bounded-degree graphs; examples include the ferromagnetic Potts model…

We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time…

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 investigate the dynamic formation of regular random graphs. In our model, we pick a pair of nodes at random and connect them with a link if both of their degrees are smaller than d. Starting with a set of isolated nodes, we repeat this…

We analyze the component evolution in inhomogeneous random intersection graphs when the average degree is close to 1. As the average degree increases, the size of the largest component in the random intersection graph goes through a phase…

The weak component generalizes the idea of connected components to directed graphs. In this paper, an exact criterion for existence of the giant weak component is derived for directed graphs with arbitrary bivariate degree distributions. In…

We generalize the poissonian evolving random graph model of Bauer and Bernard to deal with arbitrary degree distributions. The motivation comes from biological networks, which are well-known to exhibit non poissonian degree distribution. A…

Conformation-dependent design of polymer sequences can be considered as a tool to control macromolecular self-assembly. We consider the monomer unit sequences created via the modification of polymers in a homogeneous melt in accordance with…

In this paper, we investigate a stochastic model describing the time evolution of a polymerization process. A polymer is a macro-molecule resulting from the aggregation of several elementary sub-units called monomers. Polymers can grow by…

We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random…

We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical. The phase…

We study the asymptotics of large, moderate and normal deviations for the connected components of the sparse random graph by the method of stochastic processes. We obtain the logarithmic asymptotics of large deviations of the joint…

In this paper, we study random embeddings of polymer networks distributed according to any potential energy which can be expressed in terms of distances between pairs of monomers. This includes freely jointed chains, steric effects,…

We consider random graphs with a given degree sequence and show, under weak technical conditions, asymptotic normality of the number of components isomorphic to a given tree, first for the random multigraph given by the configuration model…

We introduce a very general model of an inhomogenous random graph with independence between the edges, which scales so that the number of edges is linear in the number of vertices. This scaling corresponds to the p=c/n scaling for G(n,p)…

We introduce a process where a connected rooted multigraph evolves by splitting events on its vertices, occurring randomly in continuous time. When a vertex splits, its incoming edges are randomly assigned between its offspring and a…

We examine the phase transition of polymer adsorption as well as the underlying kinetics of polymer binding from dilute solutions on a structureless solid surface. The emphasis is put on the properties of regular multiblock copolymers,…

The Glauber dynamics on the colourings of a graph is a random process which consists in recolouring at each step a random vertex of a graph with a new colour chosen uniformly at random among the colours not already present in its…