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

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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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Dates and versions

cea-03706536 , version 1 (27-06-2022)

Licence

Attribution - CC BY 4.0

Identifiers

  • HAL Id : cea-03706536 , version 1

Cite

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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