Backbone probability of planar Brownian motion
Abstract
Motivated by critical planar percolation, we investigate a ``backbone'' event of planar Brownian motion, i.e.~the existence of two disjoint subpaths on the Brownian trajectory connecting the -neighborhood of the starting point to a macroscopic distance. We show that the probability of this event is C(||)-1(1+o(1)) as 0 for some constant C∈(0,∞).
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