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

Bertrand Duplantier (1) , Yong Han (2) , Chi Nguyen (3) , Michel Zinsmeister (4)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 College of Mathematics and Statistics (Shenzen University)
3 Ho Chi Minh University of Transport, Department of Information Technology
4 IDP - Institut Denis Poisson

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]).

Domains: Physics [physics]

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