The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.
Exponential Convergence of Langevin Distributions and Their Discrete Approximations
Abstract
In this paper we consider a continuous-time method of approximating a given distribution [math] using the Langevin diffusion [math] . We find conditions under which this diffusion converges exponentially quickly to [math] or does not: in one dimension, these are essentially that for distributions with exponential tails of the form [math] , [math] , exponential convergence occurs if and only if [math] . We then consider conditions under which the discrete approximations to the diffusion converge. We first show that even when the diffusion itself converges, naive discretizations need not do so. We then consider a 'Metropolis-adjusted' version of the algorithm, and find conditions under which this also converges at an exponential rate: perhaps surprisingly, even the Metropolized version need not converge exponentially fast even if the diffusion does. We briefly discuss a truncated form of the algorithm which, in practice, should avoid the difficulties of the other forms.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Equation of State Calculations by Fast Computing Machines
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953) · The Journal of Chemical Physics · doi:10.1063/1.1699114 · Cited by 37,192
Monte Carlo sampling methods using Markov chains and their applications.
Hastings, W. K. (1970) · Biometrika · doi:10.1093/biomet/57.1.97 · Cited by 15,195
Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods
Smith, A. F. M., & Roberts, G. O. (1993) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1993.tb01466.x · Cited by 1,713
Self-citationCorrelation functions and computer simulations
Parisi, G. (1981) · Nuclear Physics B · doi:10.1016/0550-3213(81)90056-0 · Cited by 243
Cited by
Rue, H., Martino, S., & Chopin, N. (2009) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2008.00700.x · Cited by 5,279
Lindgren, F., Rue, H., & Lindström, J. (2011) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2011.00777.x · Cited by 2,708
MCMC Using Hamiltonian Dynamics
Neal, R. M. (2011) · Handbook of Markov Chain Monte Carlo · doi:10.1201/b10905-6 · Cited by 2,574
Riemann manifold langevin and hamiltonian monte carlo methods
Girolami, M., & Calderhead, B. (2011) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2010.00765.x · Cited by 1,473
Plug & Play Generative Networks: Conditional Iterative Generation of Images in Latent Space
Nguyen, A., Clune, J., Bengio, Y., Dosovitskiy, A., & Yosinski, J. (2017) · 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2017.374 · Cited by 578
Metadata
- Authors
- Roberts, G. O., & Tweedie, R. L.
- Venue
- Bernoulli
- Publisher
- JSTOR
- Published
- 1996-12
- Volume
- 2
- Issue
- 4
- Pages
- 341
- ISSN
- 1350-7265 (ISSN-L)
- OpenAlex
- W1983452151
- Cited by
- 998
- References
- 4
- FWCI
- 2.77
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Exponential Convergence of Langevin Distributions and Their Discrete Approximations. https://app.cochat.ai/papers/10.2307/3318418
- The paper
- Roberts, G. O., & Tweedie, R. L. (1996). Exponential Convergence of Langevin Distributions and Their Discrete Approximations. Bernoulli. https://doi.org/10.2307/3318418
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
