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arXiv · 1407.0269

Disconnection and level-set percolation for the Gaussian free field

Alain-Sol Sznitman
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Abstract

We study the level-set percolation of the Gaussian free field on Z^d, d bigger or equal to 3. We consider a level alpha such that the excursion-set of the Gaussian free field above alpha percolates. We derive large deviation estimates on the probability that the excursion-set of the Gaussian free field below the level alpha disconnects a box of large side-length from the boundary of a larger homothetic box. It remains an open question whether our asymptotic upper and lower bounds are matching. With the help of a recent work of Lupu, see arXiv:1402.0298, we are able to infer some asymptotic upper bounds for similar disconnection problems by random interlacements, or by simple random walk.

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BibTeXRIS

Alain-Sol Sznitman. 2014-07-01. Disconnection and level-set percolation for the Gaussian free field. https://arxiv.org/abs/1407.0269

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