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

This paper considers the limiting distribution of π λ , 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 π λ , θ indicates that there are countably many phase transitions for the limiting distribution of π λ , θ , and the critical points are λ = 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.