Large Deviations for Zeros of P(φ)2 Random Polynomials

Renjie Feng; Steve Zelditch

doi:10.1007/s10955-011-0206-y

Large Deviations for Zeros of P(φ)₂ Random Polynomials

Renjie Feng, Steve Zelditch^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We extend the results of (Zeitouni and Zelditch in Int. Math. Res. Not. 2010(20):3939-3992, 2010) on LDPs (large deviations principles) for the empirical measures of zeros of Gaussian rando polynomials s in one variable to P(φ)₂ random polynomials. The speed and rate function are the same as in the associated Gaussian case. It follows that the expected distribution of zeros in the P(φ)₂ ensembles tends to the same equilibrium measure as in the Gaussian case.

Original language	English (US)
Pages (from-to)	619-635
Number of pages	17
Journal	Journal of Statistical Physics
Volume	143
Issue number	4
DOIs	https://doi.org/10.1007/s10955-011-0206-y
State	Published - May 2011

Keywords

Large deviations
P(φ) random polynomials

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1007/s10955-011-0206-y

Cite this

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title = "Large Deviations for Zeros of P(φ)2 Random Polynomials",

abstract = "We extend the results of (Zeitouni and Zelditch in Int. Math. Res. Not. 2010(20):3939-3992, 2010) on LDPs (large deviations principles) for the empirical measures of zeros of Gaussian rando polynomials s in one variable to P(φ)2 random polynomials. The speed and rate function are the same as in the associated Gaussian case. It follows that the expected distribution of zeros in the P(φ)2 ensembles tends to the same equilibrium measure as in the Gaussian case.",

keywords = "Large deviations, P(φ) random polynomials",

author = "Renjie Feng and Steve Zelditch",

note = "Funding Information: Research partially supported by NSF grant # DMS-0904252.",

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AU - Zelditch, Steve

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Y1 - 2011/5

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AB - We extend the results of (Zeitouni and Zelditch in Int. Math. Res. Not. 2010(20):3939-3992, 2010) on LDPs (large deviations principles) for the empirical measures of zeros of Gaussian rando polynomials s in one variable to P(φ)2 random polynomials. The speed and rate function are the same as in the associated Gaussian case. It follows that the expected distribution of zeros in the P(φ)2 ensembles tends to the same equilibrium measure as in the Gaussian case.

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KW - P(φ) random polynomials

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