Work

Patterson-Sullivan measures for point processes and the reconstruction of harmonic functions

Year: 2018

Type: preprint

Abstract: The Patterson-Sullivan construction is proved almost surely to recover every harmonic function in a certain Banach space from its values on the zero set of a Gaussian analytic function on the disk. The argument relies on the slow growth of variance for linear statistics of the concerned point process. As a corollary of reconstruction result in general abstract setting, Patterson-Sullivan reconstruction of harmonic functions is obtained in real and complex hyperbolic spaces of arbitrary dimension.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1806.02306

Authors: Bufetov, Alexander I., Qiu, Yanqi

Institutions: Institut de Mathématiques de Marseille, Institut de Mathématiques de Toulouse

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2807477661

Cites: 18

Cited by: 1

Related to: 10