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Gaussian Analytic functions in the polydisk by Massaneda, Xavier; Pridhnani, Bharti is a scholarly article available to read on EtoBox.

What is Gaussian Analytic functions in the polydisk about?

We study hyperbolic Gaussian analytic functions in the unit polydisk of $\mathbb C^n$. Following the scheme previously used in the unit ball we first study the asymptotics of fluctuations of linear statistics as the directional intensities $L_j$, $j=1,\dots,n$ tend to $\infty$. Then we estimate the probability of large deviations of such linear statistics and use the estimate to prove a hole theorem. Our proofs are inspired by the methods of M. Sodin and B. Tsirelson for the one-dimensional case, and B. Shiffman and S. Zelditch for the study of the analogous problem for compact K\"ahler manifolds.

Author

Massaneda, Xavier; Pridhnani, Bharti

Published

2014

Language

EN