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<title><string language="fre"><![CDATA[Point processes, cost and the growth of rank for locally compact groups (workshop ERC Nemo Processus ponctuels et graphes aléatoires unimodulaires)]]></string></title>
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<string language="fre"><![CDATA[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 space, as the infimum of the 
average degree of a factor wiring on its points. It turns out that the 
cost of a Poisson process is maximal among point processes of the same 
density, by proving that all free processes weakly contain the Poisson. 
The cost is related to the growth of the minimal number of generators of
lattices in Lie groups. We expect that for semisimple Lie groups, the 
minimal number of generators is sublinear in the volume except for 
SL(2,R). We outline partial results in this direction and pose some open
problems. One of them is to compute the cost of the Poisson on 
hyperbolic 3-space: solving this would lead to the solution of a 40 year
old problem on Heegaard genus of hyperbolic 3-manifolds. This is joint 
work with Samuel Mellick.]]></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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