2014/03/31 by Dmitry Ioffe, Senya Shlosman, Yvan Velenik · 1 citation
Mathematics · Physics and Astronomy · #math.PR #math-ph #math.MP
paper · pdf · doi:10.1007/s00220-014-2277-5
published as Communications in Mathematical Physics 336, Issue 2, pp 905-932 (2015) · Final version to appear in Communications in Mathematical Physics (includes minor updates done at proofreading stage)
arxiv created 2015/01/12 · arxiv updated 2015/10/15
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.