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

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 [EQUATION: SEE TEXT]and the asymptotic behavior of the whole distribution for [EQUATION: SEE TEXT] for m finite with N2 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 noninteger parameter. The effects of the correlations among individual fluctuations on the extreme value statistics are discussed in our findings.