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Complex generalized integral means spectrum of drifted whole-plane SLE & LLE

Abstract : We present new exact results for the complex generalized integral means spectrum (in the sense of [DHLZ18]) for two kinds of whole-plane Loewner evolutions driven by a Lévy process: (1) The case of a Lévy process with continuous trajectories, which corresponds to Schramm-Loewner evolution SLE κ with a drift term in the Brownian driving function. There is no known result for its standard integral means spectrum, and we show that a natural path to access it goes through the introduction of the complex generalized integral means spectrum, which is obtained via the so-called Liouville quantum gravity. (2) The case of symmetric Lévy processes for which we generalize results by Loutsenko and Yermolayeva ([Lou12, LY13, LY14, LY19]).
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https://hal-cea.archives-ouvertes.fr/cea-03706536
Contributor : Emmanuelle De Laborderie Connect in order to contact the contributor
Submitted on : Monday, June 27, 2022 - 5:02:38 PM
Last modification on : Monday, July 4, 2022 - 3:26:00 AM

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  • HAL Id : cea-03706536, version 1

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Bertrand Duplantier, Yong Han, Chi Nguyen, Michel Zinsmeister. Complex generalized integral means spectrum of drifted whole-plane SLE & LLE. 2022. ⟨cea-03706536⟩

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