An Invariance Principle to Ferrari–Spohn Diffusions

Dmitry Ioffe, Senya Shlosman, Yvan Velenik

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


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 (Formula presented.). 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 in Ferrari and Spohn (Ann Probab 33(4):1302—1325, 2005) in the context of Brownian motions conditioned to stay above circular and parabolic barriers.

Original languageEnglish
Pages (from-to)905-932
Number of pages28
JournalCommunications in Mathematical Physics
Issue number2
Publication statusPublished - 2015
Externally publishedYes


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