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- W2963907540 abstract "We study the two-point correlation functions for the zeroes of systems of |${rm SO}(n+1)$|-invariant Gaussian random polynomials on |$mathbb {RP}^n$| and systems of |${rm Isom}(mathbb {R}^n)$|-invariant Gaussian analytic functions. Our result reflects the same “repelling”, “neutral”, and “attracting” short-distance asymptotic behavior, depending on the dimension, as was discovered in the complex case by Bleher, Shiffman, and Zelditch. We then prove that the correlation function for the |${rm Isom}(mathbb {R}^n)$|-invariant Gaussian analytic functions is “universal”, describing the scaling limit of the correlation function for the restriction of systems of the |${rm SO}(k+1)$|-invariant Gaussian random polynomials to any |$n$|-dimensional |$C^2$| submanifold |$M subset mathbb {RP}^k$|. This provides a real counterpart to the universality results that were proved in the complex case by Bleher, Shiffman, and Zelditch." @default.
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- W2963907540 date "2015-08-06" @default.
- W2963907540 modified "2023-09-25" @default.
- W2963907540 title "Two-Point Correlation Functions and Universality for the Zeros of Systems of SO(n+1)-invariant Gaussian Random Polynomials" @default.
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- W2963907540 doi "https://doi.org/10.1093/imrn/rnv236" @default.
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