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Abstract: We study a stochastic particle system which models the time evolution of theranking of books by online bookstores e.g., Amazon. In this system, particlesare lined in a queue. Each particle jumps at random jump times to the top ofthe queue, and otherwise stays in the queue, being pushed toward the tail everytime another particle jumps to the top. In an infinite particle limit, therandom motion of each particle between its jumps converges to a deterministictrajectory. This trajectory is actually observed in the ranking data on websites. We prove that the random empirical distribution of this particlesystem converges to a deterministic space-time dependent distribution. A coreof the proof is the law of large numbers for {\it dependent} random variables.



Autor: Kumiko Hattori, Tetsuya Hattori

Fuente: https://arxiv.org/







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