Continuous Time Markov Processes on Graphs

Jianjun Tian; Xiao-Song Lin

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Continuous Time Markov Processes on Graphs

Jianjun Tian·Xiao-Song Lin

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Abstract

We study continuous time Markov processes on graphs. The notion of frequency is introduced, which serves well as a scaling factor between any Markov time of a continuous time Markov process and that of its jump chain. As an application, we study ``multi-person simple random walks'' on a graph G with n vertices. There are n persons distributed randomly at the vertices of G. In each step of this discrete time Markov process, we randomly pick up a person and move it to a random adjacent vertex. We give estimate on the expected number of steps for these $n$ persons to meet all together at a specific vertex, given that they are at different vertices at the begininng. For regular graphs, our estimate is exact.

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Jianjun Tian, Xiao-Song Lin. 2004-10-12. Continuous Time Markov Processes on Graphs. https://arxiv.org/abs/math/0410298

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