Rate of escape of the conditioned two-dimensional simple random walk

Published 14 Jun 2023 in math.PR | (2306.08761v2)

Abstract: We prove sharp asymptotic estimates for the rate of escape of the two-dimensional simple random walk conditioned to avoid a fixed finite set. We derive it from asymptotics available for the continuous analogue of this process (cf arXiv:2102.09636), with the help of a KMT-type coupling adapted to this setup.

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References (1)

S. Popov (2021) Two-dimensional Random Walk: From Path Counting to Random Interlacements. Cambridge University Press, Cambridge.

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