Precise asymptotics of some meeting times arising from the voter model on large random regular graphs

Abstract

We consider two independent stationary random walks on large random regular graphs of degree $k\ge 3$ 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 $N(k-1)/[2(k-2)]$.

arXiv commentTo appear in Electronic Communications in Probability

References in corpus (3)

• Voter Model on Heterogeneous Graphs
• Analytical Solution of the Voter Model on Disordered Networks
• Wright-Fisher diffusions for evolutionary games with death-birth updating