We prove that the connectivity of the level sets of a wide class of smooth centred planar
Gaussian fields exhibits a phase transition at the zero level that is analogous to the phase …

Appendix A: Additional material on theory, among others, describing the connection of the
HPE to LKC regression, efficient computation of EC curves, sufficient conditions for (G 4) and …

Geometric properties of exceedance regions above a given quantile level provide
meaningful theoretical and statistical characterizations for stochastic processes defined on …

In the present paper we study three geometrical characteristics for the excursion sets of a
two-dimensional stationary isotropic random field. First, we show that these characteristics …

In this paper we consider the so-called directional perimeters of a thresholded grey-level
image. These geometrical quantities are built by considering separately the horizontal and …

The excursion set of a C 2 smooth random field carries relevant information in its various
geometric measures. From a computational viewpoint, one never has access to the …

Chemoresponsive liquid crystals (LCs) can be engineered to generate information-rich
optical responses (in the form of space–time color and brightness patterns) when they are …

Gaussian random fields are among the most important models of amorphous spatial
structures and appear across length scales in a variety of physical, biological, and …

We are interested in creating statistical methods to provide informative summaries of random
fields through the geometry of their excursion sets. To this end, we introduce an estimator for …

The study of the geometry of excursion sets of 2D random fields is a question of interest from
both the theoretical and the applied viewpoints. In this paper we are interested in the …