BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//wp-events-plugin.com//6.4.7.2//EN
TZID:Europe/Paris
X-WR-TIMEZONE:Europe/Paris
BEGIN:VEVENT
UID:0-660@lptms.universite-paris-saclay.fr
DTSTART:20190507T110000Z
DTEND:20190507T120000Z
DTSTAMP:20190430T092805Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/seminaire-du-lptm
 s-jeremie-bouttier/
SUMMARY:Séminaire du LPTMS: Jérémie Bouttier - LPTMS\, salle 201\, 2ème
  étage\, Bât 100\, Campus d'Orsay - 7 Mai 19 11:00
DESCRIPTION:\n\nLast passage percolation\, Schur processes and free fermion
 s\nJérémie Bouttier (IPhT-Saclay and ENS Lyon)\nWe consider the model of
  (directed 2D) last passage percolation (LPP)\, defined as follows. To eve
 ry site of Z^2 we assign a nonnegative random number called weight. To eve
 ry directed (north-east) path in Z^2\, we assign a weight equal to the sum
  of of the weights of the sites that it visits. If x\,y are two sites such
  that y is north-east of x\, we define the LPP time L(x\,y) as the maximal
  weight of a directed path from x to y.\n\nIn his seminal paper arXiv:math
 /9903134 [math.CO]\, Johansson considered the situation where the weights 
 are all independent and drawn according to the same geometric or exponenti
 al distribution. This case is\nintimately connected with the Totally Asymm
 etric Simple Exclusion Process (TASEP) and the so-called Corner Growth Mod
 el. He proved that the fluctuations of L(x\,y)\, when |y-x| gets large\, a
 re asymptotically governed by the Tracy-Widom GUE distribution.\n\nSeveral
  variants have been considered. In particular\, Baik and Rains considered 
 the situation where the weight array has symmetries\, for instance a refle
 ction symmetry along the main diagonal i-j=0. This is\nequivalent to consi
 dering LPP in the half-plane i-j≥0. They have shown that the asymptotic 
 fluctuations of L(x\,y)\, for x and y close to the main diagonal\, are now
  governed by the Tracy-Widom GOE or GSE\ndistribution.\n\nWhat allows to o
 btain such precise results is that\, in these models\, there exists an exa
 ct formula for the distribution of L(x\,y) in the form of a Fredholm deter
 minant or pfaffian. Such property holds for the more general class of Schu
 r processes\, which may be studied using free fermions.\n\nAfter reviewing
  these results\, I will discuss Schur processes with periodic and free bou
 ndary conditions. In the LPP picture\, this corresponds to imposing some p
 eriodicity/symmetry properties on the weight array. We will see that\, in 
 suitable asymptotic regimes\, the fluctuations of the LPP time are governe
 d by nontrivial deformations of the Tracy-Widom distributions.\n\nThis tal
 k is based on joint work with Dan Betea\, Peter Nejjar and Mirjana Vuleti
 ć.\n
CATEGORIES:seminars
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
END:VEVENT
END:VCALENDAR