A general class of mosaic random fields

2017/09/05 by Dimitri Schwab, Schwab, Dimitri, Martin Schlather +3
Computer Science · Environmental Science · Mathematics · #51M20 #60D05 #60G15 #60G60 #Data Management and Algorithms #FOS: Mathematics #Probability (math.PR) #Remote Sensing and LiDAR Applications #Soil Geostatistics and Mapping #math.PR #msc:51M20 #msc:60D05 #msc:60G15 #msc:60G60

paper · pdf · doi:10.48550/arxiv.1709.01441

arxiv created 2017/09/05 · openalex publication_date 2017/09/05 · arxiv updated 2017/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a model of a random field on a topological space M that unifies well-known models such as the Poisson hyperplane tessellation model, the random token model, and the dead leaves model. In addition to generalizing these submodels from ℝ^d to other spaces such as the d-dimensional unit sphere \mathbbS^d, our construction also extends the classical models themselves, e.g. by replacing the Poisson distribution by an arbitrary discrete distribution. Moreover, the method of construction directly produces an exact and fast simulation procedure. By investigating the covariance structure of the general model we recover various explicit correlation functions on ℝ^d and \mathbbS^d and obtain several new ones.

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