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
ABSTRACT
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
COMMENTS
Please log in or register to leave a comment