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<title><string language="fre"><![CDATA[Absence of percolation for Poisson outdegree-one graphs (workshop ERC Nemo Processus ponctuels et graphes aléatoires unimodulaires)]]></string></title>
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<string language="fre"><![CDATA[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 
conjecture by D. Daley, S. Ebert and G. Last on the absence of 
percolation for the “line-segment model”. In this planar model, a 
segment is growing from any point of the Poisson process and stops its 
growth whenever it hits another segment. The random directions are 
picked independently and uniformly on the unit sphere. This is a joint 
work with D. Dereudre and S. Le Stum.]]></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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