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PreprintarXiv licencearXiv

The Brownian bubble tea

  • Gregory F. Lawler
  • Fredrik Viklund
  • Yilin Wang
  • Catherine Wolfram
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Abstract

We use Loewner-Kufarev evolution to decompose the Brownian loop soup into a Poisson point process on Brownian bubbles which we call the Brownian bubble tea driven by ρ, where ρ is the driving measure for the Loewner chain. The only assumption on ρ is that the evolving boundaries are locally connected. This generalizes a similar disintegration result of Lawler and Werner to essentially optimal regularity, and includes foliations with finite Loewner-Kufarev energy as well as radial and whole-plane SLEκ for all κgeqslant 0. As applications, we give Brownian loop interpretations of the conformal distortion formula for Loewner-Kufarev energy and the relationships between the Loewner energy, Loewner-Kufarev energy, and the Schwarzian action.

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Cite

BibTeXRIS
BibTeX
@misc{lawler2026brownian,
  title = {{The Brownian bubble tea}},
  author = {Gregory F. Lawler and Fredrik Viklund and Yilin Wang and Catherine Wolfram},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17990},
  eprint = {2610.17990},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17990},
}
RIS
TY  - UNPB
TI  - The Brownian bubble tea
AU  - Gregory F. Lawler
AU  - Fredrik Viklund
AU  - Yilin Wang
AU  - Catherine Wolfram
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.17990
UR  - https://arxiv.org/abs/2610.17990
AB  - We use Loewner-Kufarev evolution to decompose the Brownian loop soup into a Poisson point process on Brownian bubbles which we call the Brownian bubble tea driven by ρ, where ρ is the driving measure for the Loewner chain. The only assumption on ρ is that the evolving boundaries are locally connected. This generalizes a similar disintegration result of Lawler and Werner to essentially optimal regularity, and includes foliations with finite Loewner-Kufarev energy as well as radial and whole-plane SLE_κ for all κgeqslant 0. As applications, we give Brownian loop interpretations of the conformal distortion formula for Loewner-Kufarev energy and the relationships between the Loewner energy, Loewner-Kufarev energy, and the Schwarzian action.
ER  -