# Random walk in nonhomogeneous environments: A possible approach to human and animal mobility

## TL;DR

This paper explores how nonhomogeneous environments influence random walk behaviors, especially Levy flights, and discusses implications for understanding human and animal mobility patterns.

## Contribution

It introduces a model of random walks with position-dependent jump distributions, linking anomalous diffusion to environmental heterogeneity and cognitive factors.

## Key findings

- Variable width affects anomalous diffusion types.
- Different interpretations of multiplicative noise are analyzed.
- Distribution width relates to migration and foraging behaviors.

## Abstract

The random walk process in a nonhomogeneous medium, characterised by a L\'evy stable distribution of jump length, is discussed. The width depends on a position: either before the jump or after that. In the latter case, the density slope is affected by the variable width and the variance may be finite; then all kinds of the anomalous diffusion are predicted. In the former case, only the time characteristics are sensitive to the variable width. %while the former case resolves itself to a problem with a variable jumping rate, The corresponding Langevin equation with different interpretations of the multiplicative noise is discussed. The dependence of the distribution width on position after jump is interpreted in terms of cognitive abilities and related to such problems as migration in a human population and foraging habits of animals.