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Extremal Properties for Weakly Correlated Random Variables Arising in Speckle Patterns

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Abstract

Extremal properties of the statistics of speckle pattern are studied in the context of so-called “optically smoothed” light beams of laser-matter interaction. It is shown that the asymptotic statistics of the highest intensity in a speckle pattern, which can be associated with the most intense speckles, follows a Gumbel law, which is in agreement with numerical simulations. It is found that the probability density function of the most intense speckle peaks around the value corresponding to the logarithm of the number of speckles in the considered volume times the average intensity value of the speckle pattern. This result is of great interest for nonlinear processes, like instabilities, where extreme speckles play an important role.

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Authors and Affiliations

  1. LAGA, Institut Galilée, Université Paris 13, CNRS, 93430, Villetaneuse, France

    A. Porzio

  2. Centre de Physique Théorique CPHT, CNRS, Ecole Polytechnique, 91128, Palaiseau Cedex, France

    A. Porzio & S. Hüller

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  1. A. Porzio
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  2. S. Hüller
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Correspondence to A. Porzio.

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Porzio, A., Hüller, S. Extremal Properties for Weakly Correlated Random Variables Arising in Speckle Patterns. J Stat Phys 138, 1010–1044 (2010). https://doi.org/10.1007/s10955-009-9911-1

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  • DOI: https://doi.org/10.1007/s10955-009-9911-1

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