Random soups, carpets and fractal dimensions
arXiv:1009.4782 · doi:10.1112/jlms/jdq094
Abstract
We study some properties of a class of random connected planar fractal sets induced by a Poissonian scale-invariant and translation-invariant point process. Using the second-moment method, we show that their Hausdorff dimensions are deterministic and equal to their expectation dimension. We also estimate their low-intensity limiting behavior. This applies in particular to the "conformal loop ensembles" defined via Poissonian clouds of Brownian loops for which the expectation dimension has been computed by Schramm, Sheffield and Wilson.
To appear in J. London Math. Soc
References in corpus (1)
Cited by in corpus (23)
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- On bounded-type thin local sets of the two-dimensional Gaussian free field
- Decomposition of Brownian loop-soup clusters
- Conformal Correlation Functions in the Brownian Loop Soup
- Lecture notes on the Gaussian Free Field
- Random walk loop soups and conformal loop ensembles
- The Hausdorff dimension of the CLE gasket
- Extreme nesting in the conformal loop ensemble
- Coupling the Gaussian free fields with free and with zero boundary conditions via common level lines
- A note on Loewner energy, conformal restriction and Werner's measure on self-avoiding loops
- The nested simple conformal loop ensembles in the Riemann sphere
- Sets which are not tube null and intersection properties of random measures
- Off-Criticality and the Massive Brownian Loop Soup
- Exact Correlation Functions in the Brownian Loop Soup
- Brownian Loops and Conformal Fields
- Scalar conformal primary fields in the Brownian loop soup
- Cylinders' percolation in three dimensions
- Simple CLE in Doubly Connected Domains
- Random cutout sets with spatially inhomogeneous intensities
- Fractal percolation, porosity, and dimension
- The bulk one-arm exponent for the CLE percolations
- Evolving fractal dimensions in iterative bicolored percolation
- Dimension of two-valued sets via imaginary chaos