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September 2015 Basic properties of critical lognormal multiplicative chaos
Julien Barral, Antti Kupiainen, Miika Nikula, Eero Saksman, Christian Webb
Ann. Probab. 43(5): 2205-2249 (September 2015). DOI: 10.1214/14-AOP931


We study one-dimensional exact scaling lognormal multiplicative chaos measures at criticality. Our main results are the determination of the exact asymptotics of the right tail of the distribution of the total mass of the measure, and an almost sure upper bound for the modulus of continuity of the cumulative distribution function of the measure. We also find an almost sure lower bound for the increments of the measure almost everywhere with respect to the measure itself, strong enough to show that the measure is supported on a set of Hausdorff dimension $0$.


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Julien Barral. Antti Kupiainen. Miika Nikula. Eero Saksman. Christian Webb. "Basic properties of critical lognormal multiplicative chaos." Ann. Probab. 43 (5) 2205 - 2249, September 2015.


Received: 1 April 2013; Revised: 1 March 2014; Published: September 2015
First available in Project Euclid: 9 September 2015

zbMATH: 1337.60100
MathSciNet: MR3395460
Digital Object Identifier: 10.1214/14-AOP931

Primary: 60G57
Secondary: 60G18, 83C45

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.43 • No. 5 • September 2015
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