 CARMA SEMINAR
 Speaker: Assoc Prof Murray Elder, CARMA, The University of Newcastle
 Title: A Metropolis Markov Chain algorithm to sample trivial words and compute cogrowth in finitely generated groups; or  F is not amenable.
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 21^{st} Nov 2013
 Abstract:
In this talk I will describe an algorithm to do a random walk in the space of all words equal to the identity in a finitely presented group. We prove that the algorithm samples from a well defined distribution, and using the distribution we can find the expected value for the mean length of a trivial word. We then use this information to estimate the cogrowth of the group. We ran the algorithm on several examples  where the cogrowth series in known exactly our results are in agreement with the exact results. Running the algorithm on Thompson's group $F$, we see behaviour consistent with the hypothesis that $F$ is not amenable.
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