Recursions and tightness for the maximum of the discrete, two dimensional Gaussian Free Field - Mathematics > ProbabilityReport as inadecuate




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Abstract: We consider the maximum of the discrete two dimensional Gaussian free fieldin a box, and prove the existence of a dense deterministic subsequence alongwhich the maximum, centered at its mean, is tight; this still leaves open theconjecture that tightness holds without the need for subsequences. The methodof proof relies on an argument developed by Dekking and Host for branchingrandom walks with bounded increments and on comparison results specific toGaussian fields.



Author: Erwin Bolthausen, Jean-Dominique Deuschel, Ofer Zeitouni

Source: https://arxiv.org/



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