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

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

2005-04-25

arxiv.org/abs/cond-mat/0504624v2

Phys. Rev. Lett. 95, 150601 (2005)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures, final version in PRL

Scientific paper

10.1103/PhysRevLett.95.150601

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/(\pi K)} \ln N$ and the asymptotic behavior of the whole distribution $P(m) \sim N^2 e^{-{\rm (const)} N^2 e^{-\sqrt{2\pi K} m} - \sqrt{2\pi K} m}$ 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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