English

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

Probability 2021-05-18 v3 Mathematical Physics math.MP

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 BB on every compact interval. In particular, the Airy1_1 process is absolutely continuous with respect to BB on any compact interval.

Cite

@article{arxiv.2002.08496,
  title  = {Brownian absolute continuity of the KPZ fixed point with arbitrary initial condition},
  author = {Sourav Sarkar and Bálint Virág},
  journal= {arXiv preprint arXiv:2002.08496},
  year   = {2021}
}

Comments

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

R2 v1 2026-06-23T13:47:31.669Z