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CATEGORIES:Probability
SUMMARY:Local geometry of the rough-smooth interface in th
 e two-periodic Aztec diamond. - Sunil Chhita (Durh
 am)
DTSTART;TZID=Europe/London:20200211T140000
DTEND;TZID=Europe/London:20200211T150000
UID:TALK138091AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/138091
DESCRIPTION:Random tilings of the two-periodic Aztec diamond c
 ontain three\n  macroscopic regions: frozen\, wher
 e the tilings are deterministic\; rough\,\n  where
  the correlations between dominoes decay polynomia
 lly\; smooth\,\n  where the correlations between d
 ominoes decay exponentially. In a\n  previous pape
 r\, we found that a certain averaging of the heigh
 t function\n  at the rough smooth interface conver
 ged to the extended Airy kernel\n  point process. 
 In this paper\, we augment the local geometrical p
 icture\n  at this interface by introducing well-de
 fined lattice paths which are\n  closely related t
 o the level lines of the height function. We show 
 after\n  suitable centering and rescaling that a p
 oint process from these paths\n  converge to the e
 xtended Airy kernel point process provided that th
 e\n  natural parameter associated to the two-perio
 dic Aztec\n  diamond is small enough. This is join
 t work with Kurt Johansson and\n  Vincent Beffara.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
 B
CONTACT:Perla Sousi
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