Asymptotic behaviour of near-maxima of Gaussian sequences

Let (Formula presented.) be a Gaussian random vector with a common correlation coefficient (Formula presented.), (Formula presented.), and let (Formula presented.), n � 1. For any given a > 0, define (Formula presented.), (Formula presented.) and (Formula presented.). In this paper, we obtain the limit distributions of (Kn(a)) and (Sn(a)), under the assumption that (Formula presented.) as (Formula presented.) for some (Formula presented.)