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Distribution of extremes in the fluctuations of two-dimensional equilibrium interfaces

Deok-Sun Lee
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Abstract

We investigate the statistics of the maximal fluctuation of two-dimensional Gaussian interfaces. Its relation to the entropic repulsion between rigid walls and a confined interface is used to derive the average maximal fluctuation $ \sim \sqrt{2/(πK)} \ln N$ and the asymptotic behavior of the whole distribution $P(m) \sim N^2 e^{-{\rm (const)} N^2 e^{-\sqrt{2πK} m} - \sqrt{2πK} m}$ for $m$ finite with $N^2$ and $K$ the interface size and tension, respectively. The standardized form of $P(m)$ does not depend on $N$ or $K$, but shows a good agreement with Gumbel's first asymptote distribution with a particular non-integer parameter. The effects of the correlations among individual fluctuations on the extreme value statistics are discussed in our findings.

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Deok-Sun Lee. 2005-10-06. Distribution of extremes in the fluctuations of two-dimensional equilibrium interfaces. https://doi.org/10.1103/physrevlett.95.150601

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