## On maximizing the speed of a random walk in fixed environments.(English)Zbl 1319.60092

Summary: We consider a random walk in a fixed $$\mathbb{Z}$$ environment composed of two point types: $$q$$-drifts (in which the probabiliy to move to the right is $$q$$, and $$1-q$$ to the left) and $$p$$-drifts, where $$\frac{1}{2}<q<p$$. We study the expected hitting time of a random walk at $$N$$, given the number of $$p$$-drifts in the interval $$[1,N-1]$$, and find that this time is minimized asymptotically by equally spaced $$p$$-drifts.

### MSC:

 60G50 Sums of independent random variables; random walks

### Keywords:

random walk; speed maximization; fixed environments
Full Text: