A Law of Large Numbers for the Range of Rotor Walks on Periodic Trees

W. Huss, E. Sava-Huss

2020, v.26, Issue 3, 467-486


The aim of the current work is to prove a law of large numbers for the range size of recurrent rotor walks with random initial configuration on a general class of trees, called \emph{periodic trees\/} or \emph{directed covers of graphs}. This generalizes \cite[Theorem 1.1]{huss_sava_range_speed_trees},
but the proofs are of different nature and rely on generating functions.

Keywords: rotor walk, range, rate of escape, periodic tree, Galton\tire Watson tree, generating function, law of large numbers, spectral radius, multitype branching process, recurrence, transience


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