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Further Critical Exponents

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

Abstract

We discuss the existence of some further critical exponents for high dimensional percolation like the correlation-length exponents v, \({v_2}\), as well as the gap exponent \(\varDelta \). Furthermore, we consider the two-point function exponent \(\eta \) in more detail by discussing its sharp existence in Fourier space, as well as its existence in x-space. Then we discuss the arm exponents \(\rho _\text {in}\) and \(\rho _\text {ex}\). We close this chapter by showing that \(\eta =0\) and \(\rho _\text {ex}\)=1/2 cannot simultaneously occur when \(d<6\), thus clarifying the role of the upper-critical dimension.

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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