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This is a Quantitative Study study.

October 20, 2025Open Access

One-dimensional lattice random walks in a Gaussian random potential

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Analysis reveals non-self-averaging behaviors for key quantities in random walks on a lattice, indicating distinct dynamics.

Probability current, resistance, and splitting probability show significant disparity between average and typical behavior, indicating strong effects of disorder.
For finite chains, the mean first-passage time and diffusion coefficient experience fluctuations, but become self-averaging as chain length increases.
Three models analyze transition rates based on local Gaussian random potentials impacting movement through the lattice.
Understanding these random walks offers insights into complex systems influenced by disorder, which can have broad implications for physical processes.

Kalaj et al. (2025) studied this question.

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