On the notion of dimension of unimodular discrete spaces (workshop ERC Nemo Processus ponctuels et graphes aléatoires unimodulaires)

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

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

The theme of this talk is the sampling of cluster and iterated cluster point processes. It is partially a review, mainly of the Brix–Kendall exact sampling method for cluster point processes and

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

This talk is centered on covariant dynamics on unimodular random graphs and random networks (marked graphs), namely maps from the set of vertices to itself which are preserved by graph or

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

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

We will discuss a couple of results and questions regarding the structure of large graphs. These include vertex transitive graphs, expanders and random graphs.

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

The Palm version of a stationary random measure is an important tool in probability. It is however not well known that there are in fact two Palm versions, with related but different

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