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Abstract

Invariance Principle to Ferrari-Spohn Diffusions D. Ioffe, S. Shlosman and Y. Velenik Commun. Math. Phys. 336, 905-932 (2015). We prove an invariance principle for a class of tilted $1+1$-dimensional SOS models or, equivalently, for a class of tilted random walk bridges in $\mathbb{Z}_+$. The limiting objects are stationary reversible ergodic diffusions with drifts given by the logarithmic derivatives of the ground states of associated singular Sturm-Liouville operators. In the case of a linear area tilt, we recover the Ferrari-Spohn diffusion with log-Airy drift, which was derived by Ferrari and Spohn in the context of Brownian motions conditioned to stay above circular and parabolic barriers. Key words: Invariance principle, critical prewetting, entropic repulsion, random walk, Ferrari-Spohn diffusions. Files: PDF file, Published version, bibtex