Stochastic geometry

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The stochastic geometry deals with the mathematical description and analysis of random geometric structures, such as dots or line segments, or more complicated quantities in space or plane. Random sets are an important basis .

An important application is the stereological extraction of statements about spatial structures through the statistical analysis of linear and plane sections.

Various models of statistical mechanics (in particular, lattice models in two dimensions are considered here) such as percolation theory also result in random geometric structures, which can be treated strictly mathematically using the Schramm-Löwner evolution method .

literature

  • Dietrich Stoyan , Wilfrid S. Kendall, Joseph Mecke: Stochastic Geometry and Its Applications. 2nd Edition. Wiley, Chichester et al. 1995, ISBN 0-471-95099-8 ( Wiley series in probability and statistics ).
  • OE Barndorff-Nielsen , WS Kendall and MNM van Lieshout (eds.): Stochastic Geometry. Likelihood and Computation. Chapman & Hall / CRC, Boca Raton FL et al. 1998, ISBN 0-8493-0396-6 ( Monographs on statistics and applied probability 80).