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In this article we consider transient random walks on HNN extensions offinitely generated groups. We prove that the rate of escape w.r.t. somegeneralised word length exists. Moreover, a central limit theorem with respectto the generalised word length is derived. Finally, we show that the rate ofescape, which can be regarded as a function in the finitely many parameterswhich describe the random walk, behaves as a real-analytic function in terms ofprobability measures of constant support.

Asymptotic Word Length of Random Walks on HNN Extensions