Comments and problems regarding large graphs. (workshop ERC Nemo Processus ponctuels et graphes aléatoires unimodulaires)

Random planar maps have been the subject of numerous studies over the last years. They are instance of stationary and reversible random planar maps exhibiting a non-conventional geometry at

Learning on graphs requires a graph feature representation able to discriminate among different graphs while being amenable to fast computation. The graph isomorphism problem tells us that no

Stable matchings were introduced in a seminal paper by Gale and Shapley (1962) and play an important role in economics. Following closely Holroyd, Pemantle, Peres and Schramm (2009), we shall

Bordenave and Caputo (2014) defined a notion of entropy for probability distributions on rooted graphs with finite expected degree at the root. When such a probability distribution \rho has finite BC

We shall consider Euclidean stationary point processes which have fast decay of correlations i.e., their correlation functions factorize upto an additive error decaying exponentially in the

We confirm the long-standing prediction that c=e≈2.718 is the threshold for the emergence of a non-vanishing absolutely continuous part (extended states) at zero in the limiting spectrum of the

A Poisson outdegree-one graph is a directed graph based on a marked Poisson point process such that each vertex has only one outgoing edge. We state the absence of percolation for such graphs

The cost of a vertex transitive graph is the infimum of the expected degree of an invariant random wiring of the graph. Similarly, one can define the cost of a point process on a homogeneous

In this talk we will define notions of dimension for unimodular random graphs and point-stationary point processes. These notions are in spirit similar to the Minkowski dimension and the

The notion of discrete alpha-stable point processes generalizes to point processes the notion of stable distribution. It has been introduced and studied by Davydov, Molchanov and Zuyev a few

Percolation is a model for propagation in porous media that as introduced in  1957 by Broadbent and Hammersley. An infinite graph G models the geometry of the situation and a parameter p