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

Yunbum Kook, Santosh S. Vempala

9/14/2026

cs.DScs.LGmath.PR

No confident code implementation found for this paper.

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 $n^{2.5}$, improving the previous bound of $n^{2.75}$, and matching the complexity of the abstract Speedy walk.

View on arXiv View PDF

Code Implementations

No confident code match yet

We couldn't find an author-owned or strongly-evidenced community implementation for this paper. Any repos shown below are weak matches — verify before relying on them.

No code implementations found yet.

Know of an implementation? Let us know in the comments below!

Similar Papers

Faster logconcave sampling from a cold start in high dimension

87% match2025

Sampling and Integration of Logconcave Functions by Algorithmic Diffusion

82% match2024

Chain of Log-Concave Markov Chains

81% match2023

Accelerated Mixing Time of Randomized Hamiltonian Monte Carlo

81% match2026

Algorithmic warm starts for Hamiltonian Monte Carlo

80% match2026

Faster high-accuracy log-concave sampling via algorithmic warm starts

80% match2023

Cite this paper

@article{kook2026thinshell,
  title  = {Thin-shell stability of Gaussian cooling: logconcave sampling with sesteric complexity from a cold start},
  author = {Yunbum Kook and Santosh S. Vempala},
  year   = {2026},
  eprint = {2609.15884},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2609.15884v1}
}

Add a badge to your README

Shows whether official code is linked for this paper.

[![Code of Paper](https://codeofpaper.com/badge/2609.15884.svg)](https://codeofpaper.com/paper/2609.15884)