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TZID:Europe/Paris
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BEGIN:VEVENT
UID:1-280@lptms.universite-paris-saclay.fr
DTSTART:20140711T143000Z
DTEND:20140711T153000Z
DTSTAMP:20140707T054501Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/seminaire-excepti
 onnel-du-lptms-pierpaolo-vivo/
SUMMARY:Séminaire exceptionnel du LPTMS: Pierpaolo Vivo - LPTMS\, salle 20
 1\, 2ème étage\, Bât 100\, Campus d'Orsay - 11 Juil 14 14:30
DESCRIPTION:Phase transitions in the condition number distribution of Gauss
 ian random matrices\nPierpaolo Vivo\, LPTMS\nWe study the statistics of th
 e condition number k (the ratio between largest and smallest squared singu
 lar values) of NxM Gaussian random matrices. Using a Coulomb fluid techniq
 ue\, we derive analytically and for large N its cumulative P(k&lt\;x) and 
 tail-cumulative P(k&gt\;x) distributions. We find the decay of these distr
 ibution. The left and right rate functions are calculated exactly for any 
 choice of the rectangularity parameter M/N-1. Interestingly\, they show a 
 weak non-analytic behavior at their minimum &lt\;k&gt\; (corresponding to 
 the average condition number)\, a direct consequence of a phase transition
  in the associated Coulomb fluid problem.  Matching the behavior of the r
 ate functions around &lt\;k&gt\;\, we determine exactly the scale of typic
 al fluctuations and the tails of the limiting distribution of  k. The ana
 lytical results are in excellent agreement with numerical simulations.
LOCATION:LPTMS\, salle 201\, 2ème étage\, Bât 100\, Campus d'Orsay\, 15 
 Rue Georges Clemenceau\, Orsay\, 91405\, France
GEO:48.698185;2.181768
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=15 Rue Georges Clemenceau\,
  Orsay\, 91405\, France;X-APPLE-RADIUS=100;X-TITLE=LPTMS\, salle 201\, 2è
 me étage\, Bât 100\, Campus d'Orsay:geo:48.698185,2.181768
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