Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Probability

arXiv:2308.04634 (math)
[Submitted on 9 Aug 2023]

Title:Mixing of Metropolis-Adjusted Markov Chains via Couplings: The High Acceptance Regime

Authors:Nawaf Bou-Rabee, Stefan Oberdörster
View PDF
Abstract:We present a coupling framework to upper bound the total variation mixing time of various Metropolis-adjusted, gradient-based Markov kernels in the `high acceptance regime'. The approach uses a localization argument to boost local mixing of the underlying unadjusted kernel to mixing of the adjusted kernel when the acceptance rate is suitably high. As an application, mixing time guarantees are developed for a non-reversible, adjusted Markov chain based on the kinetic Langevin diffusion, where little is currently understood.
Comments: 33 pages
Subjects: Probability (math.PR)
MSC classes: 60J05
Cite as: arXiv:2308.04634 [math.PR]
  (or arXiv:2308.04634v1 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.2308.04634
Journal reference: Electronic Journal of Probability 2024, Vol. 29, paper no. 89, 1-27
Related DOI: https://doi.org/10.1214/24-EJP1150

Submission history

From: Stefan Oberdörster [view email]
[v1] Wed, 9 Aug 2023 00:06:12 UTC (124 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.PR
< prev   |   next >
new | recent | 2023-08
Change to browse by:
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)