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

arXiv:2609.15884v1 Announce Type: cross 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.

Source: arXiv cs.LG | 2026-09-15