An invariance principle to Ferrari-Spohn diffusions
Probability
2015-10-15 v3 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1403.5073,
title = {An invariance principle to Ferrari-Spohn diffusions},
author = {Dmitry Ioffe and Senya Shlosman and Yvan Velenik},
journal= {arXiv preprint arXiv:1403.5073},
year = {2015}
}
Comments
Final version to appear in Communications in Mathematical Physics (includes minor updates done at proofreading stage)