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Introduction to Geometric Probability

Daniel A. Klain, Gian-Carlo Rota
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      The purpose of this book is to present the three basic ideas of geometrical probability, also known as integral geometry, in their natural framework. In this way, the relationship between the subject and enumerative combinatorics is more transparent, and the analogies can be more productively understood. The first of the three ideas is invariant measures on polyconvex sets. The authors then prove the fundamental lemma of integral geometry, namely the kinematic formula. Finally the analogues between invariant measures and finite partially ordered sets are investigated, yielding insights into Hecke algebras, Schubert varieties and the quantum world, as viewed by mathematicians. Geometers and combinatorialists will find this a most stimulating and fruitful story.
      Format: CONTRIBUTORS: Daniel A. Klain, Gian-Carlo Rota EAN: 9780521596541 COUNTRY: United Kingdom PAGES: WEIGHT: 230 g HEIGHT: 216 cm
      PUBLISHED BY: Cambridge University Press DATE PUBLISHED: 1997-12-11 CITY: GENRE: MATHEMATICS / Topology WIDTH: 138 cm SPINE:

      Book Themes:

      Probability and statistics

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      The purpose of this book is to present the three basic ideas of geometrical probability, also known as integral geometry, in their natural framework. In this way, the relationship between the subject and enumerative combinatorics is more transparent, and the analogies can be more productively understood. The first of the three ideas is invariant measures on polyconvex sets. The authors then prove the fundamental lemma of integral geometry, namely the kinematic formula. Finally the analogues between invariant measures and finite partially ordered sets are investigated, yielding insights into Hecke algebras, Schubert varieties and the quantum world, as viewed by mathematicians. Geometers and combinatorialists will find this a most stimulating and fruitful story.
      Format: CONTRIBUTORS: Daniel A. Klain, Gian-Carlo Rota EAN: 9780521596541 COUNTRY: United Kingdom PAGES: WEIGHT: 230 g HEIGHT: 216 cm
      PUBLISHED BY: Cambridge University Press DATE PUBLISHED: 1997-12-11 CITY: GENRE: MATHEMATICS / Topology WIDTH: 138 cm SPINE:

      Book Themes:

      Probability and statistics

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