Further Critical Exponents

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


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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