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The Derivation of the Lace Expansion via Inclusion–Exclusion

  • Markus HeydenreichEmail author
  • Remco van der Hofstad
Chapter
Part of the CRM Short Courses book series (CRMSC)

Abstract

We perform the combinatorial expansion that relies on inclusion-exclusion for the percolation two-point function \(\tau _p(x)=\mathbb {P}_{p}(0 \leftrightarrow x)\) that goes under the name lace expansion. We give a self-contained and detailed derivation of this expansion, and close this chapter by discussing how it can be effectively used, focussing in particular on the error term that arises in the inclusion-exclusion expansion.

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Mathematisches InstitutLudwig-Maximilians-Universität MünchenMünchenGermany
  2. 2.Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands

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