### Large deviations from the circular law

Gérard Ben Arous, Ofer Zeitouni (1998)

ESAIM: Probability and Statistics

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Gérard Ben Arous, Ofer Zeitouni (1998)

ESAIM: Probability and Statistics

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Arcones, Miguel A. (1997)

Electronic Journal of Probability [electronic only]

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Bai, Zhi-Dong, Hwang, Hsien-Kuei, Liang, Wen-Qi, Tsai, Tsung-Hsi (2001)

Electronic Journal of Probability [electronic only]

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Jan Gustavsson (2001)

Mathematica Bohemica

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We prove identities involving sums of Legendre and Jacobi polynomials. The identities are related to Green’s functions for powers of the invariant Laplacian and to the Minakshisundaram-Pleijel zeta function.

Li, Jie (2011)

Journal of Inequalities and Applications [electronic only]

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Anwar, Matloob, Latif, Naveed, Pečarić, J. (2009)

Journal of Inequalities and Applications [electronic only]

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Jean Picard (1997)

ESAIM: Probability and Statistics

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Basdevant, Anne-Laure, Goldschmidt, Christina (2008)

Electronic Journal of Probability [electronic only]

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Jamal Najim (2005)

ESAIM: Probability and Statistics

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A Large Deviation Principle (LDP) is proved for the family $\frac{1}{n}{\sum}_{1}^{n}\mathbf{f}\left({x}_{i}^{n}\right)\xb7{Z}_{i}^{n}$ where the deterministic probability measure $\frac{1}{n}{\sum}_{1}^{n}{\delta}_{{x}_{i}^{n}}$ converges weakly to a probability measure $R$ and ${\left({Z}_{i}^{n}\right)}_{i\in \mathbb{N}}$ are ${\mathbb{R}}^{d}$-valued independent random variables whose distribution depends on ${x}_{i}^{n}$ and satisfies the following exponential moments condition: $$\phantom{\rule{-56.9055pt}{0ex}}\underset{i,n}{sup}\mathbb{E}{\mathrm{e}}^{{\alpha}^{*}\left|{Z}_{i}^{n}\right|}\<+\infty \phantom{\rule{1.0em}{0ex}}\mathrm{forsome}\phantom{\rule{1.0em}{0ex}}0\<{\alpha}^{*}\<+\infty .$$ In this context, the identification of the rate function is non-trivial due to the absence of equidistribution. We rely on fine convex analysis to address this issue. Among...

Zang, Qing-Pei (2010)

Journal of Inequalities and Applications [electronic only]

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