2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66747We study a one parameter family of discrete Loewner evolutions driven by a random walk on the real line. We show that it converges to the stochastic Loewner evolution (SLE) under rescaling. We show that the discrete Loewner evolution satisfies Markovian-type and symmetry properties analogous to SLE, and establish a phase transition property for the discrete Loewner evolution when the parameter equals 4.21 pagesProbabilityComplex Variables60F17; 60J05; 30E20text