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PreprintCC BY 4.0arXiv

Thin-shell stability of Gaussian cooling: logconcave sampling with sesteric complexity from a cold start

  • Yunbum Kook
  • Santosh S. Vempala
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Abstract

We show that logconcave probability measures along the Gaussian cooling path have thin-shell stability, generalizing the thin-shell theorem. This result leads to improved complexity for the fundamental problem of sampling an arbitrary logconcave distribution from a cold start. For (near-)isotropic logconcave distributions, the complexity is nearly n2.5, improving the previous bound of n2.75, and matching the complexity of the abstract Speedy walk.

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Cite

BibTeXRIS
BibTeX
@misc{kook2026thinshell,
  title = {{Thin-shell stability of Gaussian cooling: logconcave sampling with sesteric complexity from a cold start}},
  author = {Yunbum Kook and Santosh S. Vempala},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15884},
  eprint = {2609.15884},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15884},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Thin-shell stability of Gaussian cooling: logconcave sampling with sesteric complexity from a cold start
AU  - Yunbum Kook
AU  - Santosh S. Vempala
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15884
UR  - https://arxiv.org/abs/2609.15884
AB  - We show that logconcave probability measures along the Gaussian cooling path have thin-shell stability, generalizing the thin-shell theorem. This result leads to improved complexity for the fundamental problem of sampling an arbitrary logconcave distribution from a cold start. For (near-)isotropic logconcave distributions, the complexity is nearly n^2.5, improving the previous bound of n^2.75, and matching the complexity of the abstract Speedy walk.
ER  -