Exact height distribution in one-dimensional Edwards-Wilkinson interface with diffusing diffusivity

2025/02/03 by David S. Dean, Satya N. Majumdar, Dean, David S. +3 · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Material Dynamics and Properties #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2502.01153

openalex publication_date 2025/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We study the height distribution of a one-dimensional Edwards-Wilkinson interface in the presence of a stochastic diffusivity D(t)=B²(t), where B(t) represents a one-dimensional Brownian motion at time t. The height distribution at a fixed point is space is computed analytically. The typical height h(x,t) at a given point in space is found to scale as t^3/4 and the distribution G(H) of the scaled height H=h/t^3/4 is symmetric but with a nontrivial shape: while it approaches a nonzero constant quadratically as H→ 0, it has a non-Gaussian tail that decays exponentially for large H. We show that this exponential tail is rather robust and holds for a whole family of linear interface models parametrized by a dynamical exponent z>1, with z=2 corresponding to the Edwards-Wilkinson model.

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