Year: 2013
Type: preprint
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 $γ< 1/2$.
Source: arXiv (Cornell University)
Author: Peterson, Jonathon
Institution: Purdue University West Lafayette
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952037662