The conformal loop ensemble nesting field
Author(s)Wilson, David B.; Miller, Jason P.; Watson, Samuel Stewart
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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.
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Mathematics
Probability Theory and Related Fields
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.
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