Exact Maximal Height Distribution of Fluctuating Interfaces - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Physical Review Letters Année : 2004

Exact Maximal Height Distribution of Fluctuating Interfaces

Résumé

We present an exact solution for the distribution P(h_m,L) of the maximal height h_m (measured with respect to the average spatial height) in the steady state of a fluctuating Edwards-Wilkinson interface in a one dimensional system of size L with both periodic and free boundary conditions. For the periodic case, we show that P(h_m,L)=L^{-1/2}f(h_m L^{-1/2}) for all L where the function f(x) is the Airy distribution function that describes the probability density of the area under a Brownian excursion over a unit interval. For the free boundary case, the same scaling holds but the scaling function is different from that of the periodic case. Numerical simulations are in excellent agreement with our analytical results. Our results provide an exactly solvable case for the distribution of extremum of a set of strongly correlated random variables.

Mots clés

Dates et versions

hal-00002293 , version 1 (02-02-2005)

Identifiants

Citer

Satya Majumdar, Alain Comtet. Exact Maximal Height Distribution of Fluctuating Interfaces. Physical Review Letters, 2004, 92 (22), pp.225501. ⟨10.1103/PhysRevLett.92.225501⟩. ⟨hal-00002293⟩
112 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More