The heavy range of randomly biased walks on trees

2018/11/06 by Andreoletti, Pierre, Diel, Roland
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1811.02226

Abstract

We focus on recurrent random walks in random environment (RWRE) on Galton-Watson trees. The range of these walks, that is the number of sites visited at some fixed time, has been studied in three different papers [AC18], [AdR17] and [dR16]. Here we study the heavy range: the number of edges visited at least α times for some integer α. The asymptotic behavior of this process when α is a power of the number of steps of the walk is given for all the recurrent cases. It turns out that this heavy range plays a crucial role in the rate of convergence of an estimator of the environment from a single trajectory of the RWRE.

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