TOPICS
Search

Ballistic Random Walk

A ballistic random walk in a nonzero direction l has a positive lower limiting linear speed in that direction almost surely,

liminf_(n->infty)(X_n·l)/n>0.

Here, liminf denotes the infimum limit. If the walk has a limiting velocity v almost surely, then

lim_(n->infty)(X_n)/n=v,

with v·l>0 almost surely. Ballisticity implies directional transience, but directional transience alone is a weaker condition.

See also

Annealed Law, Directional Transience, Law of Large Numbers, Random Walk in Random Environment

Explore with Wolfram|Alpha

References

Drewitz, A. and Ramírez, A. F. "Selected Topics in Random Walks in Random Environment." In Topics in Percolative and Disordered Systems. (Ed. A. F. Ramírez, G. Ben Arous, P. A. Ferrari, C. M. Newman, V. Sidoravicius, and M. E. Vares). New York: Springer, pp. 23-83, 2014. https://doi.org/10.1007/978-1-4939-0339-9_3.

Cite this as:

Weisstein, Eric W. "Ballistic Random Walk." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BallisticRandomWalk.html

Subject classifications