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SUMMARY:Self-avoiding Walk and Connective Constant - Li\, Z (University of
  Connecticut)
DTSTART:20150421T130000Z
DTEND:20150421T140000Z
UID:TALK59144@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:Co-author: Geoffrey Grimmett (University of Cambridge) \n\nA s
 elf-avoiding walk (SAW) is a path on a graph that revisits no vertex. The 
 connective constant of a graph is defined to be the exponential growth rat
 e of the number of n-step SAWs with respect to n. We prove that sqrt{d-1} 
 is a universal lower bound for connective constants of any infinite\, conn
 ected\, transitive\, simple\, d-regular graph. We also prove that the conn
 ective constant of a Cayley graph decreases strictly when a new relator is
  added to the group and increases strictly when a non-trivial word is decl
 ared to be a generator. I will also present a locality result regarding to
  the connective constants proved by defining a linearly increasing harmoni
 c function on Cayley graphs. In particular\, the connective constant is lo
 cal for all solvable groups. Joint work with Geoffrey Grimmett.\n \n
LOCATION:Seminar Room 1\, Newton Institute
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