Markov Paths, Loops and Fields

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

  • Yves Le Jan

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

Also part of the Ecole d'Eté Probabilit.Saint-Flour book sub series (LNMECOLE, volume 2026)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Yves Le Jan
    Pages 13-28
  3. Yves Le Jan
    Pages 29-34
  4. Yves Le Jan
    Pages 35-45
  5. Yves Le Jan
    Pages 47-56
  6. Yves Le Jan
    Pages 57-64
  7. Yves Le Jan
    Pages 65-73
  8. Yves Le Jan
    Pages 75-89
  9. 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 free 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.


60J27, 60K35; 60J45 Free field Markov loops Random Spanning trees

Authors and affiliations

  • Yves Le Jan
    • 1
  1. 1.CNRS, Département de MathématiquesUniversité Paris-SudOrsay CXFrance

Bibliographic information

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