A note on the Brownian loop measure
نویسنده
چکیده
The Brownian loop measure is a conformally invariant measure on loops that also satisfies the restriction property. In studying the Schramm-Loewner evolution (SLE), a quantity that arises is the measure of loops in a domain D that intersect both V1 and V2. If V1, V2 are nonpolar, and D = C this measure is infinite. We show the existence of a finite normalized quantity that can be used in its place. The motivation for studying this question comes from bulk SLE with boundary conditions, but this paper only discusses the loop measure.
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