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Directional Transience

Directional transience of a random walk X_n in a nonzero direction l means that its scalar projection onto that direction tends to positive infinity,

A_l={X_n·l->+infty}.

This is a path event, while a directional zero-one law states that its probability is 0 or 1. A ballistic random walk in that direction is directionally transient, but the converse need not hold.

See also

Annealed Law, Ballistic Random Walk, Random Walk in Random Environment

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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. "Directional Transience." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DirectionalTransience.html

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