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BEGIN:VEVENT
UID:0-675@lptms.universite-paris-saclay.fr
DTSTART:20190604T143000Z
DTEND:20190604T170000Z
DTSTAMP:20190507T105521Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/soutenance-de-the
 se-bertrand-lacroix-a-chez-toine-2/
SUMMARY:Soutenance de thèse: Bertrand Lacroix-à-chez-Toine - IPN-batiment
  100\, Auditoriurm - 4 Juin 19 14:30
DESCRIPTION:Soutenance de thèse:\nExtreme value statistics of strongly cor
 related systems: fermions\, random matrices and random walks\npar\nBertran
 d Lacroix-à-chez-Toine\n&nbsp\;\n\nJury:\n\n-Djalil Chafaï (CEREMADE\, U
 niversité Paris-Dauphine)\n\n-Andrea Gambassi (Scuola Internazionale Supe
 riore di Studi Avanzati\, Italy)\n\n-Jean-Marc Luck (IPhT\, CEA Saclay)\n\
 n-Satya N. Majumdar (LPTMS\, Université Paris-Sud)\n\n-Grégory Schehr (L
 PTMS\, Université Paris-Sud)\, directeur de thèse\n\n-Christophe Texier 
 (LPTMS\, Université Paris-Sud)\n\n-Patrizia Vignolo (INPHYNI\, Universit
 é de Nice-Sophia Antipolis)\n\n-Pierpaolo Vivo (King’s College London\,
  UK)\n\n&nbsp\;\n\nRésumé:\nPredicting the occurrence of extreme events 
 is a crucial issue in many contexts\, ranging from meteorology to finance.
  For independent and identically distributed (i.i.d.) random variables\, t
 hree universality classes were identified (Gumbel\, Fréchet and Weibull) 
 for the distribution of the maximum. While modelling disordered systems by
  i.i.d. random variables has been successful with Derrida's random energy 
 model\, this hypothesis fail for many physical systems which display stron
 g correlations. In this thesis\, we study three physically relevant models
  of strongly correlated random variables: trapped fermions\, random matric
 es and random walks.\nIn the first part\, we show several exact mappings b
 etween the ground state of a trapped Fermi gas and ensembles of random mat
 rix theory. The Fermi gas is inhomogeneous in the trapping potential and i
 n particular there is a finite edge beyond which its density vanishes. Goi
 ng beyond standard semi-classical techniques (such as local density approx
 imation)\, we develop a precise description of the spatial statistics clos
 e to the edge. This description holds for a large universality class of ha
 rd edge potentials. We apply these results to compute the statistics of th
 e position of the fermion the farthest away from the centre of the trap\, 
 the number of fermions in a given domain (full counting statistics) and th
 e related bipartite entanglement entropy. Our analysis also provides solut
 ions to open problems of extreme value statistics in random matrix theory.
  We obtain for instance a complete description of the fluctuations of the 
 largest eigenvalue in the complex Ginibre ensemble.\nIn the second part of
  the thesis\, we study extreme value questions for random walks. We consid
 er the gap statistics\, which requires to take explicitly into account the
  discreteness of the process. This question cannot be solved using the con
 vergence of the process to its continuous counterpart\, the Brownian motio
 n. We obtain explicit analytical results for the gap statistics of the wal
 k with a Laplace distribution of jumps and provide numerical evidence sugg
 esting the universality of these results.
CATEGORIES:seminars
LOCATION:IPN-batiment 100\, Auditoriurm\, 15 Rue Georges Clemenceau\, orsay
 \, France
GEO:48.698196;2.181773
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=15 Rue Georges Clemenceau\,
  orsay\, France;X-APPLE-RADIUS=100;X-TITLE=IPN-batiment 100\, Auditoriurm:
 geo:48.698196,2.181773
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