2007/12/10 by Marc Artzrouni, Artzrouni, Marc
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Applications (stat.AP) #Data Management and Algorithms #Diffusion and Search Dynamics #FOS: Computer and information sciences #Stochastic processes and statistical mechanics #stat.AP
paper · pdf · doi:10.48550/arxiv.0712.1477
arxiv created 2007/12/10 · openalex publication_date 2007/12/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate crossing path probabilities for two agents that move randomly in a bounded region of the plane or on a sphere (denoted R). At each discrete time-step the agents move, independently, fixed distances d1 and d2 at angles that are uniformly distributed in (0,2π). If R is large enough and the initial positions of the agents are uniformly distributed in R, then the probability of paths crossing at the first time-step is close to 2d1d2/(πA[R]), where A[R] is the area of R. Simulations suggest that the long-run rate at which paths cross is also close to 2d1d2/(πA[R]) (despite marked departures from uniformity and independence conditions needed for such a conclusion).