Tagged particle dynamics in stochastic ranking process (Q389042)

In this paper, the author studies a stochastic ranking process, which is a list of a finite number of processes driven by respective independent Poisson measures. The ranking process can be considered as positions of particles on a line, where each particle has an independent Poisson clock, whose rate depends on type of the item. If the \(i\)-th particle's Poisson clock rings, then the \(i\)-th particle jumps to the top of the list and each of the particles placed above the \(i\)-th particle descends respectively one position down. This interacting particle system is a mathematical model of the ranking in the web page of online bookstores or posting web pages. The author fastens a tag to a ``particle'' (or tags to ``particles'') and observes the motion of the ``tagged particle'' (or ``tagged particles''). A scaling limit of the tagged particle dynamics is obtained. The author also gives a scaling limit of the multi-tagged particle dynamics, in which the motion of the particles are independent.