Brownian absolute continuity of the KPZ fixed point with arbitrary initial condition

Abstract

We show that the law of the KPZ fixed point starting from arbitrary initial condition is absolutely continuous with respect to the law of Brownian motion $B$ on every compact interval. In particular, the Airy${}_1$ process is absolutely continuous with respect to $B$ on any compact interval.

arXiv comment21 pages. New references and a figure have been added, typos have been corrected, proof of Corollary 4.2 has been changed

References in corpus (8)

• Discrete polynuclear growth and determinantal processes
• The KPZ fixed point
• The directed landscape
• Scale Invariance of the PNG Droplet and the Airy Process
• PDEs for the joint distributions of the Dyson, Airy and Sine processes
• One-sided reflected Brownian motions and the KPZ fixed point
• Local Brownian property of the narrow wedge solution of the KPZ equation
• Brownian structure in the KPZ fixed point

Cited by in corpus (5)

• Three-halves variation of geodesics in the directed landscape
• One-sided reflected Brownian motions and the KPZ fixed point
• From the asymmetric simple exclusion processes to the stationary measures of the KPZ fixed point on an interval
• Disjoint optimizers and the directed landscape
• Local KPZ behavior under arbitrary scaling limits