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SUMMARY:Local graph coloring - Holroyd\, AE (Microsoft Research)
DTSTART:20150317T153000Z
DTEND:20150317T163000Z
UID:TALK58426@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-authors: Oded Schramm ()\, David B Wilson () \n\nHow can we
  color the vertices of a graph by a local rule based on i.i.d. vertex labe
 ls? More precisely\, suppose that the color of vertex v is determined by e
 xamining the labels within a finite (but perhaps random and unbounded) dis
 tance R of v\, with the same rule applied at each vertex. (The coloring is
  then said to be a finitary factor of the i.i.d. labels). Focusing on Z^d\
 , we investigate what can be said about the random variable R if the color
 ing is required to be proper\, i.e. if adjacent vertices must have differe
 nt colors. Depending on the dimension and the number of colors\, the optim
 al tail decay is either a power law\, or a tower of exponentials. I will b
 riefly discuss generalizations to shifts of finite type and finitely depen
 dent processes.\n
LOCATION:Seminar Room 1\, Newton Institute
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