Discretization error for the maximum of a Gaussian field

The paper considers the difference between (a) the true maximum of a Gaussian field on a square and (b) its maximum on a regular grid. This difference is called the discretization error. A kind of Slepian model is used to study the behavior of the field around the location of the maximum. We show that the normalized discretization error can be bounded by a quantity that converges to a uniform variable, depending on the Hessian matrix at the point of the maximum. The bound is applied to simulated and real data (satellite positioning data).