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

@article{Stadje1987TheEP, title={The exact probability distribution of a two-dimensional random walk}, author={Wolfgang Stadje}, journal={Journal of Statistical Physics}, year={1987}, volume={46}, pages={207-216} }

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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