Maximum of the integer-valued Gaussian free field

Abstract

We investigate the order of the maximum of the integer-valued Gaussian free field in two dimensions, and show that it grows logarithmically with the size of the box. Our treatment follows closely that of a recent paper by Kharash and Peled on the Fröhlich-Spencer proof of the Berezinskii-Kosterlitz-Thouless transition.

33 pages

References in corpus (3)

• Full extremal process, cluster law and freezing for the two-dimensional discrete Gaussian Free Field
• Delocalization of two-dimensional random surfaces with hard-core constraints
• The Fröhlich-Spencer Proof of the Berezinskii-Kosterlitz-Thouless Transition

Cited by in corpus (2)

• Maximum and coupling of the sine-Gordon field
• Statistical reconstruction of the Gaussian free field and KT transition