| Title: |
Weak Poincaré Inequalities for Markov chains:theory and applications |
| Authors: |
Andrieu, Christophe; Lee, Anthony; Power, Sam; Wang, Andi |
| Source: |
Andrieu, C, Lee, A, Power, S & Wang, A 2026, 'Weak Poincaré Inequalities for Markov chains : theory and applications', Annals of Applied Probability, vol. 36, no. 1, pp. 46-107. https://doi.org/10.1214/25-AAP2185 |
| Publication Year: |
2026 |
| Collection: |
University of Bristol: Bristol Reserach |
| Subject Terms: |
math.PR; stat.CO |
| Description: |
We investigate the application of Weak Poincaré Inequalities (WPI) to Markov chains to study their rates of convergence and to derive complexity bounds. At a theoretical level we investigate the necessity of the existence of WPIs to ensure L2-convergence, in particular by establishing equivalence with the Resolvent Uniform Positivity-Improving (RUPI) condition and pro-viding a counterexample. From a more practical perspective, we extend the celebrated Cheeger’s inequalities to the subgeometric setting, and further ap-ply these techniques to study random-walk Metropolis algorithms for heavy-tailed target distributions and to obtain lower bounds on pseudo-marginal algorithms. |
| Document Type: |
article in journal/newspaper |
| Language: |
English |
| Relation: |
info:eu-repo/semantics/altIdentifier/arxiv/http://arxiv.org/abs/2312.11689v1; info:eu-repo/semantics/altIdentifier/hdl/https://hdl.handle.net/1983/93cac33d-e8e3-4cfc-b882-3082ea129479 |
| DOI: |
10.1214/25-AAP2185 |
| Availability: |
https://hdl.handle.net/1983/93cac33d-e8e3-4cfc-b882-3082ea129479; https://research-information.bris.ac.uk/en/publications/93cac33d-e8e3-4cfc-b882-3082ea129479; https://doi.org/10.1214/25-AAP2185 |
| Rights: |
info:eu-repo/semantics/openAccess ; http://creativecommons.org/licenses/by/4.0/ |
| Accession Number: |
edsbas.A5E62516 |
| Database: |
BASE |