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Mean Euler Characteristic of Stationary Random Closed Sets

Jan Rataj (Charles University, Prague)
Thursday 23 February 2023 12:30–13:15 Koll. G (1532-214)
Stochastics Seminar

The translative intersection formula of integral geometry yields an expression for the mean Euler characteristic of a stationary random closed set intersected with a fixed observation window. We formulate this result in the setting of sets with positive reach and using flag measures which yield curvature measures as marginals. As an application, we consider excursion sets of stationary random fields with $C^{1,1}$ realizations, in particular, stationary Gaussian fields, and obtain results which extend those known from the literature.

NOTE: This is part of a stochastics mini-symposium consisting of two consecutive talks, whence the unusual start at 12:30.

Organised by: Stochastics Group
Contact: Markus Kiderlen Revised: 25.05.2023