The conformal loop ensemble nesting field
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440_2014_Article_604.pdf
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Author(s)
Wilson, David B.
Miller, Jason P.
Watson, Samuel Stewart
Date Issued
March 2015
Journal
Probability Theory and Related Fields
Publisher
Springer-Verlag
Citation
Miller, Jason and Samuel S. Watson, and David B. Wilson."The conformal loop ensemble nesting field." Probability Theory and Related Fields, vol. 163, no. 3, March 2015, pp. 769-801.
Version
Author's final manuscript
Abstract
The conformal loop ensemble CLE[subscript κ]with parameter 8/3<κ<8 is the canonical conformally invariant measure on countably infinite collections of non-crossing loops in a simply connected domain. We show that the number of loops surrounding an ε-ball (a random function of z and ε) minus its expectation converges almost surely as ε→0 to a random conformally invariant limit in the space of distributions, which we call the nesting field. We generalize this result by assigning i.i.d. weights to the loops, and we treat an alternate notion of convergence to the nesting field in the case where the weight distribution has mean zero. We also establish estimates for moments of the number of CLE loops surrounding two given points.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00440-014-0604-6
