Fractional Brownian motion as a rough surface

Jafar Cheraghalizadeh, Neda Valizadeh, Susan Tizdast and Morteza N. Najafi

Physica A: Statistical Mechanics and its Applications, 2024, vol. 646, issue C

Abstract: In this study we consider two dimensional fractional Brownian motion (fBM) as a rough surface, tuned by the Hurst exponent H, with a focus on the scaling relations. While this system fulfills partially the requirements for self-similar Gaussian surfaces, (like Gaussian height distribution), it shows deviations for the global features. A thorough examination of the Kondev’s hyperscaling relations is presented. The global features associated with level lines which define contour loop ensemble (CLE) are studied in terms of H. We show that in the thermodynamic limit the fractal dimension of loops (Df), the critical exponent of the distribution of loop length (τl), and the gyration radius (τr) vary linearly with H. The hyperscaling relations between these quantities however challenge this hypothesis. While Df, τl and τr fulfill partially the Kondev relations, the loop correlation exponent xl depends weakly on H, i.e. shows deviations from 12 which is hypothesized by Kondev to be super-universal for the Gaussian surfaces.

Keywords: 2D fractional Brownian motion; Rough surface; Hyperscaling relation; Hurst exponent; Fractal properties (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:646:y:2024:i:c:s0378437124004163

DOI: 10.1016/j.physa.2024.129907

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