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<title><string language="fre"><![CDATA[A stable marriage between order and disorder (workshop ERC Nemo Processus ponctuels et graphes aléatoires unimodulaires)]]></string></title>
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<string language="fre"><![CDATA[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 
matching between the cubic lattice and a stationary Poisson process (or a
determinantal point process) with higher intensity. The matched points 
form a stationary and ergodic (under lattice shifts) point process with 
unit intensity that has many remarkable properties. If the intensity of 
the Poisson process is close to one, then it very much resembles a 
Poisson process, while for large intensities it approaches the lattice. 
Moreover, the matched points form a hyperuniform and number rigid point 
process, in sharp contrast to a Poisson process. Still the pair 
correlation decays exponentially fast. The talk is based on joint work 
with M. Klatt and D. Yogeshwaran.]]></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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