PMID: 15245233Jul 13, 2004Paper

Exact maximal height distribution of fluctuating interfaces

Physical Review Letters
Satya N Majumdar, Alain Comtet

Abstract

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>0, 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.

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Citations

Dec 18, 2013·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Yan V Fyodorov, Jonathan P Keating
Jul 29, 2016·Scientific Reports·Andrew J AllstadtThomas Caraco
Jun 29, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Grégory Schehr, Satya N Majumdar
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Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ioana Bena, Satya N Majumdar
Jul 30, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Joachim Rambeau, Grégory Schehr
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