2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/230254We 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.v2: 14 pages, 2 figures, review paper to appear in C.R. Math. Rep. Acad. Sci. Canada; added brief introduction to SLE, updated acknowledgements and referencesProbability60-02 (Primary), 60F99, 60G50, 60J45, 60J65 (Secondary)text