Sub-dominant cogrowth behaviour and the viability of deciding\n amenability numerically

2016/08/24 by Murray Elder, Elder, Murray, Cameron Rogers +1 · 1 citation
Physics and Astronomy · Mathematics · #Opinion Dynamics and Social Influence #Quantum many-body systems #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1608.06703

Abstract

We critically analyse a recent numerical method due to the first author,\nRechnitzer and van Rensburg, which attempts to detect amenability or\nnon-amenability in a finitely generated group by numerically estimating its\nasymptotic cogrowth rate. We identify two potential sources of error. We then\npropose a modification of the method that enables it to easily compute\nsurprisingly accurate estimates for initial terms of the cogrowth sequence.\n

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