Loop-Erasure of Planar Brownian Motion

We use a coupling technique to prove that there exists a loop-erasure of the time-reversal of a planar Brownian motion stopped on exiting a simply connected domain, and that the loop-erased curve is a radial SLE 2 curve. This result extends to Brownian motions and Brownian excursions under certain c...

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Veröffentlicht in:	Communications in mathematical physics 2011-05, Vol.303 (3), p.709-720
1. Verfasser:	Zhan, Dapeng
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Classical and Quantum Gravitation Complex Systems Exact sciences and technology Linear and multilinear algebra, matrix theory Mathematical and Computational Physics Mathematical methods in physics Mathematical Physics Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Other topics in mathematical methods in physics Physics Physics and Astronomy Quantum Physics Relativity Theory Sciences and techniques of general use Theoretical
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Beschreibung
Zusammenfassung:	We use a coupling technique to prove that there exists a loop-erasure of the time-reversal of a planar Brownian motion stopped on exiting a simply connected domain, and that the loop-erased curve is a radial SLE 2 curve. This result extends to Brownian motions and Brownian excursions under certain conditioning in a finitely connected plane domain, and the loop-erased curve is a continuous LERW curve.
ISSN:	0010-3616 1432-0916
DOI:	10.1007/s00220-011-1234-9