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July 2020 Planar Brownian motion and Gaussian multiplicative chaos
Antoine Jego
Ann. Probab. 48(4): 1597-1643 (July 2020). DOI: 10.1214/19-AOP1399

Abstract

We construct the analogue of Gaussian multiplicative chaos measures for the local times of planar Brownian motion by exponentiating the square root of the local times of small circles. We also consider a flat measure supported on points whose local time is within a constant of the desired thickness level and show a simple relation between the two objects. Our results extend those of (Ann. Probab. 22 (1994) 566–625), and in particular, cover the entire $L^{1}$-phase or subcritical regime. These results allow us to obtain a nondegenerate limit for the appropriately rescaled size of thick points, thereby considerably refining estimates of (Acta Math. 186 (2001) 239–270).

Citation

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Antoine Jego. "Planar Brownian motion and Gaussian multiplicative chaos." Ann. Probab. 48 (4) 1597 - 1643, July 2020. https://doi.org/10.1214/19-AOP1399

Information

Received: 1 January 2019; Revised: 1 August 2019; Published: July 2020
First available in Project Euclid: 20 July 2020

zbMATH: 07224956
MathSciNet: MR4124521
Digital Object Identifier: 10.1214/19-AOP1399

Subjects:
Primary: 60J55, 60J65

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 4 • July 2020
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