Spatial tightness at the edge of Gibbsian line ensembles (Q2684874)

The aim of the authors is develop a black-box theory which shows tightness and Brownian absolute continuity of the lowest labeled curve of a Gibbsian line ensemble given tightness of its one-point marginal distribution. \par The authors consider dedicated this study for a general class of line ensembles, in which the underlying random walk measure has continuous jumps and scales diffusively to Brownian motion, and in which the interaction energy is such that a key stochastic monotonicity property hold. \par In addition, the authors apply the black-box theory to the log-gamma polymer line ensemble and obtain that the polymer free energy has transversal fluctuation exponent 2/3, as expected by KPZ universality.