# Random walks with fractally correlated traps: Stretched exponential and power law survival kinetics

Source: [Random walks with fractally correlated traps: Stretched exponential and power law survival kinetics](<https://www.sota2.com/research/paper/68fa34b51e209131ce89b781>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T20:50:53.202Z

Authors: Dan Plyukhin, Alex V. Plyukhin

Published: 2016-10-16T00:18:02.000Z

## Abstract

We consider the survival probability $f(t)$ of a random walk with a constant hopping rate $w$ on a host lattice of fractal dimension $d$ and spectral dimension $d\_s\\le 2$, with spatially correlated traps. The traps form a sublattice with fractal dimension $d\_a\<d$ and are characterized by the absorption rate $w\_a$ which may be finite (imperfect traps) or infinite (perfect traps). Initial coordinates are chosen randomly at or within a fixed distance of a trap. For weakly absorbing traps ($w\_a\\ll w$), we find that $f(t)$ can be closely approximated by a stretched exponential function over the initial stage of relaxation, with stretching exponent $\\alpha=1-(d-d\_a)/d\_w$, where $d\_w$ is the random walk dimension of the host lattice. At the end of this initial stage there occurs a crossover to power law kinetics $f(t)\\sim t^{-\\alpha}$ with the same exponent $\\alpha$ as for the stretched exponential regime. For strong absorption $w\_a\>w$, including the limit of perfect traps $w\_a\\to \\infty$, the stretched exponential regime is absent and the decay of $f(t)$ follows, after a short transient, the aforementioned power law for all times.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1610.04801>)

[PDF](<https://arxiv.org/pdf/1610.04801.pdf>)