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An invariance principle to Ferrari-Spohn diffusions

Ioffe, Dmitry
Shlosman, Senya
Published in Communications in Mathematical Physics. 2015, vol. 336, p. 905-932
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.
Keywords Invariance principleCritical prewettingEntropic repulsionRandom walkFerrari-Spohn diffusions
arXiv: 1403.5073
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IOFFE, Dmitry, SHLOSMAN, Senya, VELENIK, Yvan Alain. An invariance principle to Ferrari-Spohn diffusions. In: Communications in Mathematical Physics, 2015, vol. 336, p. 905-932. https://archive-ouverte.unige.ch/unige:34911

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Deposited on : 2014-03-24

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