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

Abstract

We study the height distribution of a one-dimensional Edwards-Wilkinson interface in the presence of a stochastic diffusivity $D(t)=B^2(t)$, 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 $H\to 0$, 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.

arXiv comment18 pages, 4 figures

References in corpus (19)

• Persistence and First-Passage Properties in Non-equilibrium Systems
• Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities
• "Diffusing diffusivity": A model for anomalous and "anomalous yet Brownian" diffusion
• Multiple Excitation of Confined Graphene Plasmons by Single Free Electrons
• Packets of Diffusing Particles Exhibit Universal Exponential Tails
• A model of non-Gaussian diffusion in heterogeneous media
• Spatial Persistence of Fluctuating Interfaces
• Generalized Langevin Equation Formulation for Anomalous Polymer Dynamics
• Active Brownian Motion with Directional Reversals
• First passage statistics for diffusing diffusivity
• Universal spectral features of different classes of random diffusivity processes
• Position distribution in a generalised run and tumble process
• Effective Perrin theory for the anisotropic diffusion of a strongly hindered rod
• Non-Gaussian diffusion near surfaces
• Brownian non-Gaussian polymer diffusion and queing theory in the mean-field limit
• Polymers critical point originates Brownian non-Gaussian diffusion
• Large Deviation in Continuous Time Random Walks
• On the distribution of estimators of diffusion constants for Brownian motion
• Large Deviations in Switching Diffusion: from Free Cumulants to Dynamical Transitions

Cited by in corpus (3)

• Dynamically emergent correlations in Brownian particles subject to simultaneous non-Poissonian resetting protocols
• Dynamically emergent correlations in a Brownian gas with diffusing diffusivity
• Shape-specific fluctuations of an active colloidal interface