2014/01/24 by Andrey Sarantsev, Sarantsev, Andrey · 1 citation
Business, Management and Accounting · Mathematics · #60H10 #60J65 #91B26 #Advanced Queuing Theory Analysis #FOS: Mathematics #Primary 60K35 #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics #secondary 60J60
paper · pdf · doi:10.48550/arxiv.1401.6255
openalex publication_date 2014/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider a finite system of competing Brownian particles on the real line. Each particle moves as a Brownian motion, with drift and diffusion coefficients depending only on its current rank relative to the other particles. A triple collision occurs if three particles are at the same position at the same moment. A simultaneous collision occurs if at a certain moment, there are two distinct pairs of particles such that in each pair, both particles occupy the same position. These two pairs of particles can overlap, so a triple collision is a particular case of a simultaneous collision. We find a necessary and sufficient condition for a.s. absense of triple and simultaneous collisions, continuing the work of Ichiba, Karatzas, Shkolnikov (2013). Our results are also valid for the case of asymmetric collisions, when the local time of collision between the particles is split unevenly between them; these systems were introduced in Karatzas, Pal, Shkolnikov (2012).