Abstract:
In joint work with Alexander Bufetov, we show that the classical Patterson-Sullivan construction can be generalized to the random setting in the theory of point processes. This construction allows us to recover the value of any Hardy function at any point of the disc from its restriction to a random configuration of the determinant point process with the Bergman kernel. This interpolation 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.
Biography:
Yanqi Qiu is Associate Professor in Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Charge de Recherche in CNRS in France (on leave). His research interests are probability, particle systems, ergodic theory, functional and harmonic analysis.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai