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- Date de réalisation : 20 Mars 2019
- Lieu de réalisation : Paris
- Durée du programme : 52 min
- Classification Dewey : Probabilités, Statistiques mathématiques, Mathématiques appliquées
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- Catégorie : Conférences
- Niveau : niveau Doctorat (LMD), Recherche
- Disciplines : Mathématiques et informatique, Probabilités
- Collections : ERC Nemo, Workshop Processus ponctuels et graphes aléatoires unimodulaires (20-22 mars 2019)
- ficheLom : Voir la fiche LOM
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- Auteur(s) : Khezeli Ali
- producteur : INRIA (Institut national de recherche en informatique et automatique)
- Editeur : INRIA (Institut national de recherche en informatique et automatique) , Baccelli François

On the notion of dimension of unimodular discrete spaces (workshop ERC Nemo Processus ponctuels et graphes aléatoires unimodulaires)
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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 for calculating the dimension. Discrete analogues of
several theorems regarding the dimension of continuum spaces are
presented; e.g., the mass distribution principle, Billingsley’s lemma,
Frostman’s lemma, and the max-flow min-cut theorem. In addition, the
notion of unimodular discrete spaces is introduced which is a common
generalization of unimodular random graphs and point-stationary point
processes. The dimension of several examples of such spaces will be
studied. Different methods for finding upper bounds and lower bounds on
the dimension will also be presented and illustrated through these
examples.
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