Asymptotic behaviour of an infinitely-many-alleles diffusion with symmetric overdominance

This paper considers the limiting distribution of πλ,θπλ,θ, the stationary distribution of the infinitely-many-alleles diffusion with symmetric overdominance (Ethier and Kurtz, 1998). In Feng (2009) the large deviation principle for πλ,θπλ,θ indicates that there are countably many phase transitions for the limiting distribution of πλ,θπλ,θ, and the critical points are λ=k(k+1),k≥1λ=k(k+1),k≥1. The asymptotic behaviours at those critical points, however, are unclear. This article provides a definite description of the critical cases.