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Let  be a centered Gaussian random field with variance function  (⋅) that attains its maximum at the unique point , and let . For  a compact subset of ℝ, the current literature explains the asymptotic tail behaviour of  under some regularity conditions including that 1 − () has a polynomial decrease to 0 as  →  . In this contribution we consider more general case that 1 − () is regularly varying at  . We extend our analysis to Gaussian random fields defined on some compact set , deriving the exact tail asymptotics of  for the class of Gaussian random fields with variance and correlation functions being regularly varying at  . A crucial novel element is the analysis of families of Gaussian random fields that do not possess locally additive dependence structures, which leads to qualitatively new types of asymptotics.

Extremes of Gaussian random fields with regularly varying dependence structure