# The exact probability distribution of a two-dimensional random walk

```@article{Stadje1987TheEP,
title={The exact probability distribution of a two-dimensional random walk},
journal={Journal of Statistical Physics},
year={1987},
volume={46},
pages={207-216}
}```
• Published 1987
• Mathematics
• Journal of Statistical Physics
A calculation is made of the exact probability distribution of the two-dimensional displacement of a particle at timet that starts at the origin, moves in straight-line paths at constant speed, and changes its direction after exponentially distributed time intervals, where the lengths of the straight-line paths and the turn angles are independent, the angles being uniformly distributed. This random walk is the simplest model for the locomotion of microorganisms on surfaces. Its weak convergence…
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