dorsal/arxiv
View SchemaMark correlations: relating physical properties to spatial distributions
| Authors | Claus Beisbart, Martin Kerscher, Klaus Mecke |
|---|---|
| Categories | |
| ArXiv ID | physics/0201069 |
| URL | https://arxiv.org/abs/physics/0201069 |
Abstract
Mark correlations provide a systematic approach to look at objects both distributed in space and bearing intrinsic information, for instance on physical properties. The interplay of the objects' properties (marks) with the spatial clustering is of vivid interest for many applications; are, e.g., galaxies with high luminosities more strongly clustered than dim ones? Do neighbored pores in a sandstone have similar sizes? How does the shape of impact craters on a planet depend on the geological surface properties? In this article, we give an introduction into the appropriate mathematical framework to deal with such questions, i.e. the theory of marked point processes. After having clarified the notion of segregation effects, we define universal test quantities applicable to realizations of a marked point processes. We show their power using concrete data sets in analyzing the luminosity-dependence of the galaxy clustering, the alignment of dark matter halos in gravitational $N$-body simulations, the morphology- and diameter-dependence of the Martian crater distribution and the size correlations of pores in sandstone. In order to understand our data in more detail, we discuss the Boolean depletion model, the random field model and the Cox random field model. The first model describes depletion effects in the distribution of Martian craters and pores in sandstone, whereas the last one accounts at least qualitatively for the observed luminosity-dependence of the galaxy clustering.
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"abstract": "Mark correlations provide a systematic approach to look at objects both\ndistributed in space and bearing intrinsic information, for instance on\nphysical properties. The interplay of the objects\u0027 properties (marks) with the\nspatial clustering is of vivid interest for many applications; are, e.g.,\ngalaxies with high luminosities more strongly clustered than dim ones? Do\nneighbored pores in a sandstone have similar sizes? How does the shape of\nimpact craters on a planet depend on the geological surface properties? In this\narticle, we give an introduction into the appropriate mathematical framework to\ndeal with such questions, i.e. the theory of marked point processes. After\nhaving clarified the notion of segregation effects, we define universal test\nquantities applicable to realizations of a marked point processes. We show\ntheir power using concrete data sets in analyzing the luminosity-dependence of\nthe galaxy clustering, the alignment of dark matter halos in gravitational\n$N$-body simulations, the morphology- and diameter-dependence of the Martian\ncrater distribution and the size correlations of pores in sandstone. In order\nto understand our data in more detail, we discuss the Boolean depletion model,\nthe random field model and the Cox random field model. The first model\ndescribes depletion effects in the distribution of Martian craters and pores in\nsandstone, whereas the last one accounts at least qualitatively for the\nobserved luminosity-dependence of the galaxy clustering.",
"arxiv_id": "physics/0201069",
"authors": [
"Claus Beisbart",
"Martin Kerscher",
"Klaus Mecke"
],
"categories": [
"physics.data-an",
"astro-ph",
"cond-mat.stat-mech",
"math.PR"
],
"title": "Mark correlations: relating physical properties to spatial distributions",
"url": "https://arxiv.org/abs/physics/0201069"
},
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