摘要： In a recent joint work with Alexander Bufetov, we show that the classical Patterson-Sullivan construction in conformal dynamical system can be generalized to the random setting in the theory of point processes. This construction allows us to recover the value of any harmonic function with additional regularity at any point of the disc from its restriction to a random configuration of the determinant point process with the Bergman kernel. Similar result is then extended to real and complex hyperbolic spaces of higher dimension. Recovering continuous functions by the Patterson-Sullivan construction is also shown to be possible in more general Gromov hyperbolic spaces. This work is a further research after our complete resolution of the Lyons-Peres completeness conjecture for determinantal point processes.

报告人简介：
2017-now: Associate Professor (tenured), Insitute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences.
2015?2017 CNRS, Charg?e de Recherche (tenured), on leave from 2017/09, Universit?e Paul Sabatier (Toulouse III).
2013?2015 Postdoc, Aix-Marseille Universit?e.
在世界著名期刊 J. London Math. Soc.，Math. Ann.，Compositio Mathematica，J. Funct. Anal.，Adv. Math.，等杂志上发表文章.