We consider two independent stationary random walks on large random regular graphs of degree with N vertices. On these graphs, the exponential approximations of the meeting times are known to follow from existing methods and form a basis for the voter model’s diffusion approximations. The main result of this note improves the exponential approximations to an explicit form such that the first moments are asymptotically equivalent to .
"Precise asymptotics of some meeting times arising from the voter model on large random regular graphs." Electron. Commun. Probab. 26 1 - 13, 2021. https://doi.org/10.1214/21-ECP373