# An Invariance Principle to Ferrari–Spohn Diffusions

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Dmitry Ioffe, Senya Shlosman, Yvan Velenik

Dmitry Ioffe, Senya Shlosman, Yvan Velenik

**29/1/15**Published in : Communications in Mathematical Physics, doi:10.1007/s00220-014-2277-5

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 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 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.