Current Developments in Mathematics

Volume 2016

Edge fluctuations of limit shapes

Pages: 47 – 110

DOI: http://dx.doi.org/10.4310/CDM.2016.v2016.n1.a2

Author

Kurt Johansson (Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden)

Abstract

In random tiling and dimer models we can get various limit shapes which give the boundaries between different types of phases. The shape fluctuations at these boundaries give rise to universal limit laws, in particular the Airy process. We survey some models which can be analyzed in detail based on the fact that they are determinantal point processes with correlation kernels that can be computed.We also discuss which type of limit laws that can be obtained.

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Supported by the Knut and Alice Wallenberg Foundation grant KAW:2010.0063 and by the Swedish Science Research Council (VR).