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

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

4 pages, 4 figures, final version in PRL

References in corpus (1)

• Extreme Fluctuations in Small-Worlds with Relaxational Dynamics

Cited by in corpus (10)

• Universal correlators and distributions as experimental signatures of 2+1 Kardar-Parisi-Zhang growth
• Kardar-Parisi-Zhang universality class in 2+1 dimensions: Universal geometry-dependent distributions and finite-time corrections
• Global fluctuations in physical systems: a subtle interplay between sum and extreme value statistics
• Initial pseudo-steady state & asymptotic KPZ universality in semiconductor on polymer deposition
• Temperature effect on (2+1) experimental Kardar-Parisi-Zhang growth
• Maximal and minimal height distributions of fluctuating interfaces
• Crossing intervals of non-Markovian Gaussian processes
• Maximum relative height of one-dimensional interfaces : from Rayleigh to Airy distribution
• Universal statistical properties of poker tournaments
• On the weak scaling of the contact distance between two fluctuating interfaces with system size