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Weakly anomalous diffusion with non-Gaussian propagators.

J C Cressoni¹, G M Viswanathan, A S Ferreira

¹Departamento de Física e Química, FCFRP, Universidade de São Paulo, Ribeirão Preto, SP 14040-903, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 26, 2012

Summary

This summary is machine-generated.

This study presents an analytical solution for weakly anomalous diffusion in complex systems. The model explains diffusion with a Hurst exponent of 1/2 but non-Gaussian statistics, offering insights into random walk behavior.

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Area of Science:

Complex systems analysis
Statistical physics
Stochastic processes

Background:

Complex systems often exhibit diffusion with a Hurst exponent (H) of approximately 1/2, yet display non-Gaussian statistical properties.
This combination of characteristics in diffusion processes remains poorly understood in many empirical observations.

Purpose of the Study:

To provide an exact analytical solution for a random walk model exhibiting weakly anomalous diffusion.
To explain diffusion with H ≈ 1/2 and non-Gaussian statistics, addressing a gap in understanding complex system dynamics.

Main Methods:

Development of an exact analytical solution for a non-Markovian random walk model.
Mathematical analysis of the model's statistical properties and diffusion characteristics.

Main Results:

The proposed non-Markovian random walk model yields weakly anomalous diffusion.
The model accurately reproduces diffusion with a Hurst exponent H = 1/2.
A non-Gaussian propagator is derived, consistent with empirical observations in complex systems.

Conclusions:

The analytical solution offers a theoretical framework for understanding diffusion with H ≈ 1/2 and non-Gaussian statistics.
This work contributes to the broader understanding of anomalous diffusion in complex systems.
The findings have implications for modeling various phenomena in physics and other scientific domains.