Recursions and tightness for the maximum of the discrete, two dimensional Gaussian Free Field

Details Recursions and tightness for the maximum of the discrete, two dimensional Gaussian Free Field Recursions and tightness for the maximum of the discrete, two dimensional Gaussian Free Field

2010-05-28

arxiv.org/abs/1005.5417v2

Mathematics

Probability

Proof significantly shortened following a remark of Y. Peres

Scientific paper

We consider the maximum of the discrete two dimensional Gaussian free field in a box, and prove the existence of a (dense) deterministic subsequence along which the maximum, centered at its mean, is tight; this still leaves open the conjecture that tightness holds without the need for subsequences. The method of proof relies on an argument developed by Dekking and Host for branching random walks with bounded increments and on comparison results specific to Gaussian fields.

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