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The infinite two-sided loop-erased random walk

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The loop-erased random walk (LERW) in $ \Z^d, d \geq 2$, is obtained by erasing loops chronologically from simple random walk. In this paper we show the existence of the… Click to show full abstract

The loop-erased random walk (LERW) in $ \Z^d, 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.

Keywords: loop erased; erased random; two sided; random walk

Journal Title: Electronic Journal of Probability
Year Published: 2020

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