Limit theory for geometric statistics of point processes having fast decay of correlations
Supplement to “Limit theory for geometric statistics of point processes having fast decay of
correlations”. This supplement contains various auxiliary facts needed in the proofs. These …
correlations”. This supplement contains various auxiliary facts needed in the proofs. These …
Lipschitz-Killing curvatures of excursion sets for two-dimensional random fields
H Biermé, E Di Bernardino, C Duval, A Estrade - 2019 - projecteuclid.org
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 …
two-dimensional stationary isotropic random field. First, we show that these characteristics …
Surface area and volume of excursion sets observed on point cloud based polytopic tessellations
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 …
geometric measures. From a computational viewpoint, one never has access to the …
Statistics for Gaussian random fields with unknown location and scale using Lipschitz‐Killing curvatures
In the present article we study the average of Lipschitz‐Killing (LK) curvatures of the
excursion set of a stationary isotropic Gaussian field X on ℝ 2. The novelty is that the field …
excursion set of a stationary isotropic Gaussian field X on ℝ 2. The novelty is that the field …
Goodness-of-fit tests for complete spatial randomness based on Minkowski functionals of binary images
We propose a class of goodness-of-fit tests for complete spatial randomness (CSR). In
contrast to standard tests, our procedure utilizes a transformation of the data to a binary …
contrast to standard tests, our procedure utilizes a transformation of the data to a binary …
Pixel isotropy test based on directional perimeters
M Abaach, H Biermé, E Di Bernardino, A Estrade - Spatial Statistics, 2024 - Elsevier
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 …
image. These geometrical quantities are built by considering separately the horizontal and …
Normal convergence of nonlocalised geometric functionals and shot-noise excursions
R Lachièze-Rey - The Annals of Applied Probability, 2019 - JSTOR
This article presents a complete second-order theory for a large class of geometric
functionals on homogeneous Poisson input. In particular, the results do not require the …
functionals on homogeneous Poisson input. In particular, the results do not require the …
Empirical modelling and analysis of phase noise in OFDM systems
Q Duan, H Du, J Xue, F Li - IET Communications, 2024 - Wiley Online Library
Based on empirical data of an orthogonal frequency division multiplexing system in realistic
environments of next‐generation cellular networks, a new analytical model of phase noise …
environments of next‐generation cellular networks, a new analytical model of phase noise …
Betti numbers of Gaussian excursions in the sparse regime
Random field excursions is an increasingly vital topic within data analysis in medicine,
cosmology, materials science, etc. This work is the first detailed study of their Betti numbers …
cosmology, materials science, etc. This work is the first detailed study of their Betti numbers …
On the geometry of excursion sets: theoretical and computational guarantees
R Cotsakis - 2024 - theses.hal.science
The excursion set EX (u) of a real-valued random field X on R^ d at a threshold level u∈ R is
the subset of the domain R^ d on which X exceeds u. Thus, the excursion set is random, and …
the subset of the domain R^ d on which X exceeds u. Thus, the excursion set is random, and …