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SUMMARY:Scaling limits for a dynamic model of 2D Young diagrams - Funaki\,
  T (Tokyo)
DTSTART:20100104T113000Z
DTEND:20100104T123000Z
UID:TALK22167@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We construct dynamics of two-dimensional Young diagrams\, whic
 h are naturally associated with their grandcanonical ensembles\, by allowi
 ng the creation and annihilation of unit squares located at the boundary o
 f the diagrams. The grandcanonical ensembles\, which were introduced by Ve
 rshik (Func. Anal. Appl.\, '96)\, are uniform measures under conditioning 
 on their area.  We then show that\, as the averaged size of the diagrams d
 iverges\, the corresponding height variable converges to a solution of a c
 ertain non-linear partial differential\nequation under a proper space-time
  scaling.  The stationary solution of the limit equation is identified wit
 h the so-called Vershik curve. We also discuss the corresponding dynamic f
 luctuation problem under a non-equilibrium situation\, and derive stochast
 ic partial differential equations in the limit.  We study both uniform and
  restricted uniform statistics for the Young diagrams. \n\nThis is a joint
  work with Makiko Sasada (Univ Tokyo) and the paper on the part of the hyd
 rodynamic limit is available: \n\narXiv:0909.5482.\n
LOCATION:Seminar Room 1\, Newton Institute
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