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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Self-avoiding Walk and Connective Constant - Li\,
Z (University of Connecticut)
DTSTART;TZID=Europe/London:20150421T140000
DTEND;TZID=Europe/London:20150421T150000
UID:TALK59042AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/59042
DESCRIPTION:Co-author: Geoffrey Grimmett (University of Cambri
dge) \n\nA self-avoiding walk (SAW) is a path on a
graph that revisits no vertex. The connective con
stant of a graph is defined to be the exponential
growth rate of the number of n-step SAWs with resp
ect to n. We prove that sqrt{d-1} is a universal l
ower bound for connective constants of any infinit
e\, connected\, transitive\, simple\, d-regular gr
aph. We also prove that the connective constant of
a Cayley graph decreases strictly when a new rela
tor is added to the group and increases strictly w
hen a non-trivial word is declared to be a generat
or. I will also present a locality result regardin
g to the connective constants proved by defining a
linearly increasing harmonic function on Cayley g
raphs. In particular\, the connective constant is
local for all solvable groups. Joint work with Geo
ffrey Grimmett.\n \n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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