Complex generalized integral means spectrum of drifted whole-plane SLE & LLE
Résumé
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).
Domaines
Physique [physics]Origine | Fichiers produits par l'(les) auteur(s) |
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