Non-Gaussianity and varying scaling exponents in long-range dependent motion

Stochastic processes with long-range dependent correlations naturally emerge
in many systems when degrees of freedom are integrated out, apart from the
dynamic of the (tracer) particle of interest. In non-equilibrium situations,
the resulting overdamped dynamics often corresponds to fractional Brownian
motion (FBM).

In disordered systems the observed displacement probability density is often
non-Gaussian, and FBM-type processes display scaling exponents varying in time
or space. This talk introduces diffusion models with stochastically [1,2] and
deterministically [3,4] varying diffusion coefficients and scaling exponents.
Apart from the more traditional Mandelbrot-van Ness formulation of FBM, Levy's
non-equilibrium approach via a fractional integral will also be discussed.
Various applications to experimental data will be introduced.

References:

[1] A. V. Chechkin, F. Seno, R. Metzler, and I. M. Sokolov, Brownian yet
non-Gaussian diffusion: from superstatistics to subordination of diffusing
diffusivities, Phys. Rev. X 7, 021002 (2017).

[2] W. Wang, F. Seno, I. M. Sokolov, A. V. Chechkin, and R. Metzler,
Unexpected crossovers in correlated random-diffusivity processes, New J. Phys.
22, 083041 (2020).
W. Wang, A. G. Cherstvy, A. V. Chechkin, S. Thapa, F. Seno, X. Liu, and
R. Metzler, Fractional Brownian motion with random diffusivity: emerging
residual nonergodicity below the correlation time, J. Phys. A 53, 474001 (2020).

[3] W. Wang, M. Balcerek, K. Burnecki, A. V. Chechkin, S. Janusonis, J. Slezak,
T. Vojta, A. Wylomanska, and R. Metzler, Memory-multi-fractional Brownian motion
with continuous correlations, Phys. Rev. Res. 5, L032025 (2023).

[4] J. Slezak and R. Metzler, Minimal model of diffusion with time changing
Hurst exponent, J. Phys. A 56, 35LT01 (2023).