Maximal Points and Gaussian Fields

Let (Wi)i be i.i.d. random variables with a continuous density ‰ having support on a compact subset S ‰ d . Subject to mild regularity conditions on the boundary of S we develop the limit theory for the number of maximal points in (Wi) n=1 as well as for point measures induced by the maximal points. Cumulant expansions show that the finite dimensional distributions of the point measures induced by the maximal points converge to those of a Gaussian field whose covariance kernel depends only on the behavior of ‰ on the boundary of S. This yields Gaussian limits for record values and Johnson-Mehl growth processes.

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