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The probability that planar loop-erased random walk uses a given edge

   
@article{ECP2908,
	author = {Gregory Lawler},
	title = {The probability that planar loop-erased random walk uses a given edge},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {19},
	year = {2014},
	keywords = {},
	abstract = {We give a new proof of a result of Rick Kenyon that the probability that an edge in the middle of an $n \times n$ square is used in a loop-erased walk connecting opposite sides is of order $n^{-3/4}$.  We, in fact, improve the result by showing that this estimate is correct up to multiplicative constants.},
	pages = {no. 51, 1-13},
	issn = {1083-589X},
	doi = {10.1214/ECP.v19-2908},    
        url = {http://ecp.ejpecp.org/article/view/2908}}