We study a one parameter family of discrete Löwner evolutions driven by a random walk on the real line. We show that it converges to the stochastic Löwner evolution (SLE) under rescaling. We show that the discrete Löwner evolution satisfies Markovian-type and symmetry properties analogous to SLE, and establish a phase transition property for the discrete Löwner evolution when the parameter equa...

Abstract Quantum random walks have been much studied recently, largely due to their highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum random walk on the line: the use of multiple quantum “coins” in order to diminish the effects of interference between paths. We find solutions to this system in terms of the single coin random ...