Mathematics > Probability
[Submitted on 12 Apr 2018 (v1), last revised 7 Jun 2023 (this version, v3)]
Title:Stein kernels and moment maps
View PDFAbstract:We describe a construction of Stein kernels using moment maps, which are solutions to a variant of the Monge-Ampère equation. As a consequence, we show how regularity bounds on these maps control the rate of convergence in the classical central limit theorem, and derive new rates in Kantorovitch-Wasserstein distance in the log-concave situation, with explicit polynomial dependence on the dimension.
Submission history
From: Max Fathi [view email][v1] Thu, 12 Apr 2018 19:24:30 UTC (12 KB)
[v2] Sat, 16 Jun 2018 15:59:24 UTC (14 KB)
[v3] Wed, 7 Jun 2023 10:38:28 UTC (14 KB)
Current browse context:
math.PR
References & Citations
Bookmark
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
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.