We study numerically and analytically the spectrum of incidence matrices of random labeled graphs on N vertices: any pair of vertices is connected by an edge with probability p. We give twoâ€¦ (More)

We study both numerically and analytically what happens to a random graph of average connectivity Î± when its leaves and their neighbors are removed iteratively up to the point when no leaf remains.â€¦ (More)

The statistics of meanders is studied in connection with the Temperley-Lieb algebra. Each (multi-component) meander corresponds to a pair of reduced elements of the algebra. The assignment of aâ€¦ (More)

We present an exact analysis of two conductor-insulator transitions in the random graph model where low connectivity means high impurity concentration. The adjacency matrix of the random graph isâ€¦ (More)

We study the height of the delta peak at 0 in the spectrum of incidence matrices of random trees. We show that the average fraction of the spectrum occupied by the eigenvalue 0 in a large random treeâ€¦ (More)

The Asymmetric Simple Exclusion Process (ASEP) plays the role of a paradigm in Non-Equilibrium Statistical Mechanics. We review exact results for the ASEP obtained by Bethe Ansatz and put emphasis onâ€¦ (More)

We conjecture that meanders are governed by the gravitational version of a c = âˆ’4 two-dimensional conformal field theory, allowing for exact predictions for the meander configuration exponent Î± = âˆšâ€¦ (More)

We study the statistics of semi-meanders, i.e. configurations of a set of roads crossing a river through n bridges, and possibly winding around its source, as a toy model for compact folding ofâ€¦ (More)

The statistics of meander and related problems are studied as particular realizations of compact polymer chain foldings. This paper presents a general discussion of these topics, with a particularâ€¦ (More)

We present a new derivation of the spectral gap of the totally asymmetric exclusion process on a half-filled ring of size L by using the Bethe Ansatz. We show that, in the large L limit, the Betheâ€¦ (More)