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Entropy and drift for word metric on relatively hyperbolic groups. (arXiv:1811.10849v2 [math.GR] UPDATED)
来源于:arXiv
We are interested in the Guivarc'h inequality for admissible random walks on
finitely generated relatively hyperbolic groups, endowed with a word metric. We
show that for random walks with finite super-exponential moment, if this
inequality is an equality, then the Green distance is roughly similar to the
word distance, generalizing results of Blach{\`e}re, Ha{\"i}ssinsky and Mathieu
for hyperbolic groups [4]. Our main application is for relatively hy-perbolic
groups with respect to virtually abelian subgroups of rank at least 2. We show
that for such groups, the Guivarc'h inequality with respect to a word distance
and a finitely supported random walk is always strict. 查看全文>>