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PreprintCC BY-NC-ND 4.0arXiv

The KPZ Upper-Tail Field as a KPZ Fixed Point with Brownian Initial Data

  • Ruixuan Zhang
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Abstract

The KPZ upper-tail field introduced by Liu and Zhang arises as the scaling limit of the narrow-wedge KPZ fixed point in a microscopic neighborhood of a conditioned large height. In this paper, we give a direct probabilistic identification of the upper-tail field. We identify the grounded positive-time sector with the KPZ fixed point started from the two-sided Brownian V-profile Bts(2x)−2|x|, while the negative-time sector is represented through an explicit exponential tilt of the same evolution. The argument uses the directed-landscape variational structure and the local Brownian comparison under upper-tail conditioning. As consequences of these representations, we recover probabilistically the positive- and negative-time large-scale limits of the KPZ upper-tail field.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026uppertail,
  title = {{The KPZ Upper-Tail Field as a KPZ Fixed Point with Brownian Initial Data}},
  author = {Ruixuan Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26424},
  eprint = {2609.26424},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26424},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - The KPZ Upper-Tail Field as a KPZ Fixed Point with Brownian Initial Data
AU  - Ruixuan Zhang
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26424
UR  - https://arxiv.org/abs/2609.26424
AB  - The KPZ upper-tail field introduced by Liu and Zhang arises as the scaling limit of the narrow-wedge KPZ fixed point in a microscopic neighborhood of a conditioned large height. In this paper, we give a direct probabilistic identification of the upper-tail field. We identify the grounded positive-time sector with the KPZ fixed point started from the two-sided Brownian V-profile B_ts(2x)−2|x|, while the negative-time sector is represented through an explicit exponential tilt of the same evolution. The argument uses the directed-landscape variational structure and the local Brownian comparison under upper-tail conditioning. As consequences of these representations, we recover probabilistically the positive- and negative-time large-scale limits of the KPZ upper-tail field.
ER  -