Details

Autor(en) / Beteiligte

• Dauvergne, Duncan

Titel

Last passage isometries for the directed landscape

Ist Teil von

• Probability theory and related fields, 2023-06, Vol.186 (1-2), p.391-437

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2023

Quelle

EBSCOhost Business Source Ultimate

Beschreibungen/Notizen

• Consider the restriction of the directed landscape L ( x , s ; y , t ) to a set of the form { x 1 , ⋯ , x k } × { s 0 } × R × { 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.