NOTE ON BOLTHAUSEN-DEUSCHEL-ZEITOUNI'S PAPER ON THE ABSENCE OF A WETTING TRANSITION FOR A PINNED HARMONIC CRYSTAL IN DIMENSIONS THREE AND LARGER

Loren Coquille (1) , Piotr Miłós (2)

1 IF - Institut Fourier
2 UW - University of Warsaw

The article [1] provides a proof of the absence of a wetting transition for the discrete Gaussian free field conditioned to stay positive, and undergoing a weak delta-pinning at height 0. The proof is generalized to the case of a square pinning-potential replacing the delta-pinning, but it relies on a lower bound on the probability for the field to stay above the support of the potential, the proof of which appears to be incorrect. We provide a modified proof of the absence of a wetting transition in the square-potential case, which does not require the aforementioned lower bound. An alternative approach is given in a recent paper by Giacomin and Lacoin [2].

Domaines: Probabilités [math.PR]

Loren Coquille, Piotr Miłós. NOTE ON BOLTHAUSEN-DEUSCHEL-ZEITOUNI'S PAPER ON THE ABSENCE OF A WETTING TRANSITION FOR A PINNED HARMONIC CRYSTAL IN DIMENSIONS THREE AND LARGER. 2017. ⟨hal-01483051⟩