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A Note on Universality of Gaussian Analytic Functions on Symmetric Spaces | | Andrew Ledoan
; Marco Merkli
; Shannon Starr
; | | Date: |
9 Mar 2010 | | Abstract: | We consider random analytic functions on the classical symmetric spaces: the
spherical, planar and hyperbolic planes. We suppose that the coefficients of
the random power series are i.i.d., random variables, but not necessarily
Gaussian. But we do assume that they have the same covariance as the Gaussian
analytic functions, which is stationary, in a projective sense, with respect to
isometries. We show that as one takes the isometries converging to $infty$ in
a suitable sense, the functions converge in distribution to Gaussian analytic
functions. This is also true of their zeros, including the correlations of
zeros. The proof is elementary. | | Source: | arXiv, 1003.1951 | | Services: | Forum | Review | PDF | Favorites | |
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