The tail of the length of an excursion in a trap of random size

Abstract

Consider a random walk with a drift to the right on $\{0,\dots ,k\}$ where $k$ is random and geometrically distributed. We show that the tail $P[T>t]$ of the length $T$ of an excursion from $0$ decreases up to constants like $t^{-\varrho }$ for some $\varrho >0$ but is not regularly varying. We compute the oscillations of $t^{\varrho }P[T>t]$ as $t\to \infty$ explicitly.

References in corpus (3)

• Biased random walks on random graphs
• Regularity of the speed of biased random walk in a one-dimensional percolation model
• Einstein relation for random walk in a one-dimensional percolation model

Cited by in corpus (1)

• Biased Random Walk on Spanning Trees of the Ladder Graph