Extreme slowdowns for one-dimensional excited random walks

Jonathon Peterson

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arXiv · 1312.4983

Extreme slowdowns for one-dimensional excited random walks

Jonathon Peterson

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Abstract

We study the asymptotics of the probabilities of extreme slowdown events for transient one-dimensional excited random walks. That is, if $\{X_n\}_{n\geq 0}$ is a transient one-dimensional excited random walk and $T_n = \min\{ k: \, X_k = n\}$, we study the asymptotics of probabilities of the form $P(X_n \leq n^γ)$ and $P(T_{n^γ} \geq n )$ with $γ< 1$. We show that there is an interesting change in the rate of decay of these extreme slowdown probabilities when $γ< 1/2$.

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BibTeX RIS

Jonathon Peterson. 2016-06-11. Extreme slowdowns for one-dimensional excited random walks. https://arxiv.org/abs/1312.4983

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