2024/04/17 by Enzo Orsingher, Orsingher, Enzo, Manfred Marvin Marchione +1
Engineering · #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Particle Dynamics in Fluid Flows #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2404.11521
openalex publication_date 2024/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a planar random motion (X(t),Y(t)) with orthogonal directions which can turn clockwise, counterclockwise and reverse its direction each with a different probability. The support of the process is given by a time-varying square and the singular distributions on the boundary and the diagonals of the square are obtained. In the interior of the support, we study the hydrodynamic limit of the distribution. We then investigate the time T(t) spent by the process moving vertically and the joint distribution of (T(t),Y(t)). We prove that, in the hydrodynamic limit, the process (X(t),Y(t)) spends half the time moving vertically.