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

arXiv: https://arxiv.org/abs/2609.15884 · HTML: https://mlsanity.com/paper/2609.15884/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 33 references that are in the map.
- First posted on arXiv 14 Sep 2026.

## Builds on (most cited first, 11 of 11)

- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [Structured Logconcave Sampling with a Restricted Gaussian Oracle](https://mlsanity.com/paper/2010.03106/) (2020)
- [In-and-Out: Algorithmic Diffusion for Sampling Convex Bodies](https://mlsanity.com/paper/2405.01425/) (2024)
- [Sampling and Integration of Logconcave Functions by Algorithmic Diffusion](https://mlsanity.com/paper/2411.13462/) (2024)
- [Reducing Isotropy and Volume to KLS: Faster Rounding and Volume Algorithms](https://mlsanity.com/paper/2008.02146/) (2020)
- [Faster logconcave sampling from a cold start in high dimension](https://mlsanity.com/paper/2505.01937/) (2025)
- [Zeroth-order Logconcave Sampling](https://mlsanity.com/paper/2507.18021/) (2025)
- [Gaussian Cooling and O*(n^3) Algorithms for Volume and Gaussian Volume](https://mlsanity.com/paper/1409.6011/) (2014)
- [R'enyi-infinity constrained sampling with d3 membership queries](https://mlsanity.com/paper/2407.12967/) (2024)
- [A unified complexity bound for logconcave sampling](https://mlsanity.com/paper/2606.12694/) (2026)
- [Spectral Gaps of Hit-and-Run and Coordinate Hit-and-Run](https://mlsanity.com/paper/2608.16878/) (2026)

## Abstract (arXiv)

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.