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The scaling limit of Fomin's identity for two paths in the plane

Michael J. Kozdron
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Abstract

We review some recently completed research that establishes the scaling limit of Fomin's identity for loop-erased random walk on Z^2 in terms of the chordal Schramm-Loewner evolution (SLE) with parameter 2. In the case of two paths, we provide a simplified proof of the identity for loop-erased random walk and simple random walk, and prove directly that the corresponding identity holds for chordal SLE(2) and Brownian motion. We also include a brief introduction to SLE and discussion of the relationship between SLE(2) and loop-erased random walk.

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Michael J. Kozdron. 2008-02-10. The scaling limit of Fomin's identity for two paths in the plane. https://arxiv.org/abs/math/0703615

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