N-sided Radial Schramm-Loewner Evolution

Abstract

We use the interpretation of the Schramm-Loewner evolution as a limit of path measures tilted by a loop term in order to motivate the definition of $n$-radial SLE going to a particular point. In order to justify the definition we prove that the measure obtained by an appropriately normalized loop term on $n$-tuples of paths has a limit. The limit measure can be described as $n$ paths moving by the Loewner equation with a driving term of Dyson Brownian motion. While the limit process has been considered before, this paper shows why it naturally arises as a limit of configurational measures obtained from loop measures.

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Cited by in corpus (1)

• On Loewner chains driven by semimartingales and complex Bessel-type SDEs