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The infinite two-sided loop-erased random walk (1802.06667v1)
Published 19 Feb 2018 in math.PR
Abstract: The loop-erased random walk (LERW) in $ \Zd, d \geq 2$, is obtained by erasing loops chronologically from simple random walk. In this paper we show the existence of the two-sided LERW which can be considered as the distribution of the LERW as seen by a point in the "middle" of the path.