Dimensions of Level Sets

  • Sourav Chatterjee
Part of the Springer Monographs in Mathematics book series (SMM)


This chapter contains some byproducts of the author’s analysis of Gaussian fields, especially extremal fields. The notions of “dimension” and “implicit dimension” of level sets of Gaussian fields are defined, together with techniques for computing these dimensions. Applications to understanding the near-maximal regions of polymer models and spin glasses are worked out.


  1. Daviaud, O.: Extremes of the discrete two-dimensional Gaussian free field. Ann. Probab. 34(3), 962–986 (2006) CrossRefzbMATHMathSciNetGoogle Scholar
  2. Hu, X., Miller, J., Peres, Y.: Thick points of the Gaussian free field. Ann. Probab. 38(2), 896–926 (2010) CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Sourav Chatterjee
    • 1
  1. 1.Department of StatisticsStanford UniversityStanfordUSA

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