Restricting SLE(8/3 ) to an annulus

Robert O. Bauer

Research output: Contribution to journalArticlepeer-review

Abstract

We study the probability that chordal SLE8 / 3 in the unit disk from exp (i x) to 1 avoids the disk of radius q centered at zero. We find the initial/boundary value problem satisfied by this probability as a function of x and a = ln q, and show that asymptotically as q tends to 1 this probability decays like exp (- c x / (1 - q)) with c = 5 π / 8 for 0 < x ≤ π. We also give a representation of this probability as a multiplicative functional of a Legendre process.

Original languageEnglish (US)
Pages (from-to)1165-1188
Number of pages24
JournalStochastic Processes and their Applications
Volume117
Issue number9
DOIs
StatePublished - Sep 2007
Externally publishedYes

Keywords

  • Annulus
  • Conformal invariance
  • Elliptic functions
  • Restriction
  • SLE

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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