Hausdorff dimensions for shared endpoints of disjoint geodesics in the directed landscape

2019/12/09 by Bates, Erik, Ganguly, Shirshendu, Hammond, Alan · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1912.04164

Abstract

Within the Kardar-Parisi-Zhang universality class, the space-time Airy sheet is conjectured to be the canonical scaling limit for last passage percolation models. In recent work arXiv:1812.00309 of Dauvergne, Ortmann, and Virág, this object was constructed and shown to be the limit after parabolic correction of one such model: Brownian last passage percolation. This limit object, called the directed landscape, admits geodesic paths between any two space-time points (x,s) and (y,t) with s

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