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<title><string language="fre"><![CDATA[On the notion of dimension of unimodular discrete spaces (workshop ERC Nemo Processus ponctuels et graphes aléatoires unimodulaires)]]></string></title>
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<string language="fre"><![CDATA[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.]]></string></description>
<keyword><string language="fre"><![CDATA[processus ponctuels]]></string></keyword><keyword><string language="fre"><![CDATA[graphes aléatoires]]></string></keyword><keyword><string language="fre"><![CDATA[dynamique des réseaux stochastiques]]></string></keyword><keyword><string language="fre"><![CDATA[modélisation réseau]]></string></keyword>
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<date><dateTime>2019-03-20</dateTime></date>
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<string language="fre"><![CDATA[Workshop Processus ponctuels et graphes aléatoires unimodulaires (20-22 mars 2019)]]></string>
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