In this talk I will present a survey of the connections between canonical metrics and random point processes on a complex algebraic variety X. When the variety X has positive Kodaira dimension,

In this talk, we present a non-asymptotic bound on the L2 distance between the spectrum of the probability matrix of a random graph and the spectrum of the integral operator. Then, we study the random

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

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

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

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

This talk is devoted to clustering problems. It amounts to partitionning a set of given points or the nodes of a given graph, in such a way that the groups are as homogeneous as possible. After

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

Some themes inspired from number theory have been playing an important role in holomorphic and algebraic dynamics (iteration of rational mappings) in the past ten years. In these lectures I would

Some themes inspired from number theory have been playing an important role in holomorphic and algebraic dynamics (iteration of rational mappings) in the past ten years. In these lectures I would

Some themes inspired from number theory have been playing an important role in holomorphic and algebraic dynamics (iteration of rational mappings) in the past ten years. In these lectures I would