Last passage isometries for the directed landscape

• 成果类型: Article
• 署名作者: Dauvergne, Duncan
• 署名单位: University of Toronto
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01173-6
• 发表日期: 2023
• 页码: 391-437
• 关键词: random-walks

摘要

Consider the restriction of the directed landscape L(x, s; y, t) to a set of the form {x(1), . . . , x(k)} x {s(0)} x R x {t(0)}. We show that on any such set, the directed landscape is given by a last passage problem across k locally Brownian functions. The k functions in this last passage isometry are built from certain marginals of the extended directed landscape. As applications of this construction, we show that the Airy difference profile is locally absolutely continuous with respect to Brownian local time, that the KPZ fixed point started from two narrow wedges has a Brownian-Bessel decomposition around its cusp point, and that the directed landscape is a function of its geodesic shapes.