le (1h1m15s)

# Résultats de recherche

**38**

## On the modified Palm version (workshop ERC Nemo

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 interpretations. For lack of better terms, call the well known version standard and the less known version modified. In this talk we shall focus on the modified Palm version and its interpretation. The concepts of shift-coupling and mass-stationarity will play a key role Voir la vidéole (39m26s)

## Entropic inequalities for unimodular networks (workshop ERC Nemo *Processus* *ponctuels* et graphes aléatoires unimodulaires

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le (55m6s)

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

We will discuss a couple of results and questions regarding the structure of large graphs. These include vertex transitive graphs, expanders and random graphs.
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le (43m18s)

## Spectral embedding for graph classification (workshop ERC Nemo *Processus* *ponctuels* et graphes aléatoires unimodulaires)

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 fast representation of graphs is known if we require the representation to be both invariant to nodes permutation and able to discriminate two non-isomorphic graphs. Most graph representations explored so far require to be invariant. We explore new graph representations by relaxing this constraint. We present a generic embedding of graphs relying on spectral graph theory ...
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le (59m49s)

## Sampling cluster point processes: a review (workshop ERC Nemo *Processus* *ponctuels* et graphes aléatoires unimodulaires)

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 its adaptation by Moller and Rasmussen to Hawkes branching point processes on the real line with light-tail fertility rate. A formal proof via Laplace transforms of the validity of the method in terms of general clusters that are not necessarily point processes fits this purpose and allows to include the exact sampling of Boolean ...
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le (52m52s)

## Absence of percolation for Poisson outdegree-one graphs (workshop ERC Nemo *Processus* *ponctuels* et graphes aléatoires unimodulaires)

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 satisfying two assumptions. The Shield assumption roughly says that the graph is locally determined with possible random horizons. The Loop assumption ensures that any forward branch merges on a loop provided that the Poisson point process is augmented with a finite collection of well-chosen points. This result allows to solve a ...
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le (56m5s)

## Eternal family trees and dynamics on unimodular random graphs (workshop ERC Nemo *Processus* *ponctuels* et graphes aléatoires unimodulaires)

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 network isomorphisms. Such dynamics are referred to as vertex-shifts here. These dynamics have point-shifts on point processes as a subclass. First we give a classification of vertex-shifts on unimodular random networks. Each such vertex-shift partitions the vertices into a collection of connected components and foils. The latter are discrete analogues the stable manifold ...
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le (51m43s)

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

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 Hausdorff dimension. The key point in the definitions is the use of the mass transport principle which is used indispensably and distinguishes this view point from the previous notions which are defined in the literature. The connections of these definitions to volume growth and other notions of dimension are also discussed, which provide a toolset ...
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le (43m39s)

## A stable marriage between order and disorder (workshop ERC Nemo *Processus* *ponctuels* et graphes aléatoires unimodulaires)

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 first discuss a few basic properties of stable matchings between two discrete point sets (resp. point processes) in Euclidean space, where the points prefer to be close to each other. For comparison we also discuss stable transports from Lebesgue measure to point processes. In the second part of the talk we consider a stable ...
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le (50m47s)