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Journal Articles Annales Henri Poincaré Year : 2023

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 Duplantier et al. (Commun Math Phys 359(3):823–868, 2018)) 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 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 (J Phys A Math Theor 47(16):165202, 2014, J Phys A Math Theor 52(43):435202, 2019).
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Dates and versions

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

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Bertrand Duplantier, Yong Han, Chi Nguyen, Michel Zinsmeister. Complex generalized integral means spectrum of drifted whole-plane SLE & LLE. Annales Henri Poincaré, 2023, 25, pp.425-479. ⟨10.1007/s00023-023-01300-6⟩. ⟨cea-03706536⟩
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