The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Time to Reach Stationarity in the Bernoulli–Laplace Diffusion Model
Abstract
Consider two urns, the left containing n red balls, the right containing n black balls. At each time a ball is chosen at random in each urn and the two balls are switched. We show it takes $\tfrac{1} {4}n\log n + cn$ switches to mix up the urns. The argument involves lifting the urn model to a random walk on the symmetric group and using the Fourier transform (which in turn involves the dual Hahn polynomials). The methods apply to other “nearest neighbor” walks on two-point homogeneous spaces.
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
Biggs, N. (1974) · doi:10.1017/cbo9780511608704 · Cited by 2,940
Cited by
Group representations in probability and statistics
Diaconis, P. (1988) · doi:10.1214/lnms/1215467407 · Cited by 1,381
Self-citationGeometric Bounds for Eigenvalues of Markov Chains
Diaconis, P., & Stroock, D. (1991) · The Annals of Applied Probability · doi:10.1214/aoap/1177005980 · Cited by 882
Self-citationLectures on finite Markov chains
Saloff-Coste, L. (1997) · Lecture Notes in Mathematics · doi:10.1007/bfb0092621 · Cited by 382
Metadata
- Authors
- Diaconis, P., & Shahshahani, M.
- Venue
- SIAM Journal on Mathematical Analysis
- Published
- 1987-01
- Volume
- 18
- Issue
- 1
- Pages
- 208-218
- ISSN
- 0036-1410 (ISSN-L)
- 1095-7154
- OpenAlex
- W2138412601
- Cited by
- 160
- References
- 1
- FWCI
- 2.94
- 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: Time to Reach Stationarity in the Bernoulli–Laplace Diffusion Model. https://app.cochat.ai/papers/10.1137/0518016
- The paper
- Diaconis, P., & Shahshahani, M. (1987). Time to Reach Stationarity in the Bernoulli–Laplace Diffusion Model. SIAM Journal on Mathematical Analysis. https://doi.org/10.1137/0518016
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.
