Exact statistics of complex zeros for Gaussian random polynomials with real coefficients
- 7 August 1996
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 29 (15) , 4417-4423
- https://doi.org/10.1088/0305-4470/29/15/014
Abstract
K-point correlations of complex zeros for Gaussian ensembles of random polynomials of order N with real coefficients (GRPRC) are calculated exactly, following an approach of Hannay for the case of Gaussian random polynomials with complex coefficients (GRPCC). It is shown that in the thermodynamic limit of Gaussian random holomorphic functions all the statistics converge to their GRPCC counterparts as one moves off the real axis, while close to the real axis the two cases are essentially different. Special emphasis is given to one- and two-point correlation functions in various regimes.Keywords
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