2020/06/08 by Tomoyuki Ichiba, Ioannis Karatzas, Ichiba, Tomoyuki +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #60J60 (Primary) 60J55 #60K35 (Secondary) #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.PR #msc:60J55 #msc:60J60 #msc:60K35
paper · pdf · doi:10.48550/arxiv.2006.04970
39 pages, 5 figures
openalex publication_date 2020/06/08 · arxiv created 2021/08/21 · arxiv updated 2021/08/24 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We study systems of three interacting particles, in which drifts and variances are assigned by rank. These systems are "degenerate": the variances corresponding to one or two ranks can vanish, so the corresponding ranked motions become ballistic rather than diffusive. Depending on which ranks are allowed to "go ballistic" the systems exhibit markedly different behavior which we study in some detail. Also studied are stability properties for the resulting planar process of gaps between successive ranks.