Airy wanderer line ensembles

Abstract

In (J. Stat. Phys. 132, 275-290, 2008) Borodin and Péché introduced a generalization of the extended Airy kernel based on two infinite sets of parameters. For an arbitrary choice of parameters we construct determinantal point processes on ${\mathbb{R}}^2$ for these generalized kernels. In addition, for a subset of the parameter space we show that the point processes can be lifted to line ensembles on $\mathbb{R}$, which satisfy the Brownian Gibbs property. Our ensembles generalize the wanderer line ensembles introduced by Corwin and Hammond in (Invent. Math. 195, 441-508, 2014).

76 pages, 8 figures. The second version has modified Definition 2.16, Lemma 2.17, Proposition 2.18 and the proof of Theorem 1.5. In addition, a few typos have been corrected