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SUMMARY:Competitive erosion is conformally invariant - Peres\, Y (Microsof
 t Research)
DTSTART:20150616T080000Z
DTEND:20150616T090000Z
UID:TALK59826@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:Co-author: Shirshendu Ganguly (University of Washington) \n\nW
 e study a graph-theoretic model of interface dynamics called {f competiti
 ve erosion}. Each vertex of the graph is occupied by a particle\, which ca
 n be either red or blue. New red and blue particles are emitted alternatel
 y from their respective sources and perform random walk. On encountering a
  particle of the opposite color they remove it and occupy its position. Th
 is is a finite competitive version of the celebrated Internal DLA growth m
 odel first analyzed by Lawler\, Bramson and Griffeath in 1992. We establis
 h conformal invariance of competitive erosion on discretizations of smooth
 \, simply connected planar domains. This is done by showing that at statio
 narity\, with high probability the blue and the red regions are separated 
 by an orthogonal circular arc on the disc and more generally by a hyperbol
 ic geodesic. (Joint work with Shirshendu Ganguly\, available at http://arx
 iv.org/abs/1503.06989 ).\n
LOCATION:Seminar Room 1\, Newton Institute
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