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Markov Paths, Loops and Fields

École d'Été de Probabilités de Saint-Flour XXXVIII – 2008

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  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2026)

Part of the book sub series: École d'Été de Probabilités de Saint-Flour (LNMECOLE)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-viii
  2. Loop Measures

    • Yves Le Jan
    Pages 13-28
  3. Geodesic Loops

    • Yves Le Jan
    Pages 29-34
  4. Poisson Process of Loops

    • Yves Le Jan
    Pages 35-45
  5. The Gaussian Free Field

    • Yves Le Jan
    Pages 47-56
  6. Energy Variation and Representations

    • Yves Le Jan
    Pages 57-64
  7. Decompositions

    • Yves Le Jan
    Pages 65-73
  8. Loop Erasure and Spanning Trees

    • Yves Le Jan
    Pages 75-89
  9. Reflection Positivity

    • Yves Le Jan
    Pages 91-97
  10. Back Matter

    Pages 115-124

About this book

The purpose of these notes is to explore some simple relations between Markovian path and loop measures, the Poissonian ensembles of loops they determine, their occupation fields, uniform spanning trees, determinants, and Gaussian Markov fields such as the fre field. These relations are first studied in complete generality for the finite discrete setting, then partly generalized to specific examples in infinite and continuous spaces.

Authors and Affiliations

  • CNRS, Département de Mathématiques, Université Paris-Sud, Orsay CX, France

    Yves Le Jan

Bibliographic Information

  • Book Title: Markov Paths, Loops and Fields

  • Book Subtitle: École d'Été de Probabilités de Saint-Flour XXXVIII – 2008

  • Authors: Yves Le Jan

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-21216-1

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2011

  • Softcover ISBN: 978-3-642-21215-4Published: 06 July 2011

  • eBook ISBN: 978-3-642-21216-1Published: 06 July 2011

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 124

  • Number of Illustrations: 9 b/w illustrations

  • Topics: Probability Theory and Stochastic Processes, Potential Theory

Buy it now

Buying options

eBook USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access