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arXiv · 1403.5073

An invariance principle to Ferrari-Spohn diffusions

Dmitry Ioffe·Senya Shlosman·Yvan Velenik
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Abstract

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 by Ferrari and Spohn in the context of Brownian motions conditioned to stay above circular and parabolic barriers.

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Dmitry Ioffe, Senya Shlosman, Yvan Velenik. 2015-01-12. An invariance principle to Ferrari-Spohn diffusions. https://doi.org/10.1007/s00220-014-2277-5

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