On the Meeting Time for Two Random Walks on a Regular Graph

arXiv1408.2005MaRDI QIDQ6253791

Bhaskar Krishnamachari, Yizhen Zhang, Zihan Tan

Publication date: 8 August 2014

Abstract: We provide an analysis of the expected meeting time of two independent random walks on a regular graph. For 1-D circle and 2-D torus graphs, we show that the expected meeting time can be expressed as the sum of the inverse of non-zero eigenvalues of a suitably defined Laplacian matrix. We also conjecture based on empirical evidence that this result holds more generally for simple random walks on arbitrary regular graphs. Further, we show that the expected meeting time for the 1-D circle of size $N$ is $Theta(N^2)$, and for a 2-D $NimesN$ torus it is $Theta(N^{2}logN)$.

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