Excited Brownian Motions

2008/10/20 by Olivier Raimond, Bruno Schapira, Raimond, Olivier +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0810.3538

openalex publication_date 2008/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a natural continuous time version of excited random walks, introduced by Norris, Rogers and Williams about twenty years ago. We obtain a necessary and sufficient condition for recurrence and for positive speed. This is analogous to results for excited (or cookie) random walks.

Citations

• Excited random walk in three dimensions has positive speed
• Excited random walk in two dimensions has linear speed

Related

• Excited Brownian motions as limits of excited random walks
• On the Speed of an Excited Asymmetric Random Walk
• A functional limit theorem for for excited random walks
• Excited random walk in two dimensions has linear speed
• Positively and negatively excited random walks on integers, with branching processes