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:0-892@lptms.universite-paris-saclay.fr
DTSTART;TZID=Europe/Paris:20231207T143000
DTEND;TZID=Europe/Paris:20231207T180000
DTSTAMP:20231129T080136Z
URL:https://www.lptms.universite-paris-saclay.fr/seminars/soutenance-de-th
 ese-li-gan-2/
SUMMARY:Soutenance de thèse : Li Gan - Petit amphi\, bâtiment Pascal n° 
 530 - 7 Déc 23 14:30
DESCRIPTION:Algebraic Area of Lattice Random Walks and Exclusion Statistics
  Join Zoom Meetinghttps://universite-paris-saclay-fr.zoom.us/j/9575529780
 4?pwd=NWk4TW8rdjd4d0oyZjlpSHNia01KZz09Meeting ID: 957 5529 7804Passcode: 3
 93787 We focus on the enumeration of closed lattice random walks accordin
 g to their algebraic area\, with connections to quantum exclusion statisti
 cs\, as well as the combinatorics of generalized Dyck and Motzkin paths. F
 irst\, taking the closed square lattice walks as an example\, we review th
 e concept of the algebraic area and its connections to the Hofstadter mode
 l. Then\, we introduce two approaches for the algebraic area enumeration. 
 The first approach relies on the computation of the secular determinant of
  the Hofstadter Hamiltonian and its relation to the exclusion statistics. 
 Precisely\, the coefficients of the secular determinant are interpreted in
  terms of partition functions with exclusion parameter $g=2$. The algebrai
 c area enumeration is obtained in terms of the associated cluster coeffici
 ents. The second approach involves a direct computation of the trace of th
 e $n$th power of the Hofstadter matrix\, where $n$ is the length of the wa
 lks. We study the combinatorics of periodic Dyck paths and obtain explicit
  expressions for counting Dyck paths with a fixed number of up steps start
 ing from each floor\, which provide a combinatorial interpretation to the 
 factor in the algebraic area enumeration formula obtained in the first app
 roach. Then\, we study the closed random walks on a honeycomb lattice and 
 establish a correspondence to a system of particles obeying a mixture of $
 g=1$ (fermions) and $g=2$ exclusion statistics\, together with the connect
 ion to the combinatorics of periodic Motzkin paths. Furthermore\, we exten
 d the algebraic area concept to closed cubic lattice walks and map the enu
 meration onto the cluster coefficients of three types of particles obeying
  $g=1$\, $g=1$\, and $g=2$ exclusion statistics\, respectively\, with the 
 constraint that the numbers of $g=1$ exclusion particles of the two types 
 are equal.Jury : Cyril Banderier\, Cyril Furtlehner\, Brian Hopkins (rappo
 rteur)\, Stéphane Ouvry (directeur de thèse)\, Valentina Ros\, Clément 
 Sire\, Stephan Wagner (rapporteur).
CATEGORIES:seminars
LOCATION:Petit amphi\, bâtiment Pascal n° 530\, rue André Rivière\, Ors
 ay\, 91405\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=rue André Rivière\, Orsay
 \, 91405\, France;X-APPLE-RADIUS=100;X-TITLE=Petit amphi\, bâtiment Pasca
 l n° 530:geo:0,0
END:VEVENT
BEGIN:VTIMEZONE
TZID:Europe/Paris
X-LIC-LOCATION:Europe/Paris
BEGIN:STANDARD
DTSTART:20231029T020000
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
END:STANDARD
END:VTIMEZONE
END:VCALENDAR