Introduction and Motivation

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


We give a mathematical introduction to percolation, and state the main questions. We introduce the various critical percolation thresholds, and argue that the most interesting behavior occurs close to it. We introduce critical exponents that describe the system at or close to the phase transition, and the role of the upper critical dimension. Finally, we explain basic techniques (in particular, the BK and FKG inequalities and Russo’s formula) and describe our aim of these lecture notes.

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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