On the linear combination of the Gaussian and student’s tt random field and the integral geometry of its excursion sets

In this paper, a random field, denoted by GTβν, is defined from the linear combination of two independent random fields, one is a Gaussian random field and the second is a student’s tt random field with νν degrees of freedom scaled by ββ. The goal is to give the analytical expressions of the expected Euler–Poincaré characteristic of the GTβν excursion sets on a compact subset SS of R2R2. The motivation comes from the need to model the topography of 3D rough surfaces represented by a 3D map of correlated and randomly distributed heights with respect to a GTβν random field. The analytical and empirical Euler–Poincaré characteristics are compared in order to test the GTβν model on the real surface.

► Introducing the linear combination of Gaussian and student’s tt random fields.
► Computing analytically the expected Euler characteristic intensities on R2R2.
► Testing the random field on a real 3D rough surface.