Spectral Formula for the Expected First Meeting Time of Diverse Random Walks on a Graph

The first meeting time is defined by the time it takes for multiple mobile agents starting random walks from different nodes on a graph to first meet at the same node. Understanding the characteristics of the first meeting time is important to design an efficient rendezvous algorithm on a graph. In the previous work, we analyzed two mobile agents performing simple random walks with the same transition probability, and derived the expected value of the first meeting time. In this paper, we derive the spectral formula for the expected first meeting time of diverse random walk agents with different transition probabilities and movement frequencies.