The DOI matches its Crossref record; 19 of the 21 references it cites were found in a registry or an index.
A diffusion limit for a class of randomly-growing binary trees
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“so that the expected compression is asymptotically well-approximated by n/log2n”
From A statistical test suite for random and pseudorandom number generators for cryptographic applications (2000) · cites this paper as Aldous and Shields (1988)
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
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“which implies that a central Hmit theorem holds for the number of words in the Lempel-Ziv compression.”
From A statistical test suite for random and pseudorandom number generators for cryptographic applications (2000) · cites this paper as Aldous and Shields (1988)
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Citations
Cites
The Art of Computer Programming
Knuth, D. E. (1968) · Cited by 16,000
Doob, J. L., & Doob, J. L. (1953) · CERN Document Server (European Organization for Nuclear Research) · Cited by 9,053
A universal algorithm for sequential data compression
Ziv, J., & Lempel, A. (1977) · IEEE Transactions on Information Theory · doi:10.1109/tit.1977.1055714 · Cited by 5,456
Ross, S. M. (1982) · Cited by 3,812
The Theory of Stochastic Processes
Cox, D. R., Miller, H. D., Weiss, G., & Shuler, K. (1966) · Physics Today · doi:10.1063/1.3047872 · Cited by 3,324
The Theory of Stochastic Processes III
Gihman, I. I., & Skorohod, A. V. (1979) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-1-4615-8065-2 · Cited by 1,184
The Art of Computer Programming, Vol. 2
Knuth, D. E. (1981) · Medical Entomology and Zoology · Cited by 886
Oriented Percolation in Two Dimensions
Durrett, R. T. (1984) · The Annals of Probability · doi:10.1214/aop/1176993140 · Cited by 366
Stopping Times and Tightness. II
Aldous, D. (1989) · The Annals of Probability · doi:10.1214/aop/1176991417 · Cited by 343
Self-citationCoding theorems for individual sequences
Ziv, J. (1978) · IEEE Transactions on Information Theory · doi:10.1109/tit.1978.1055911 · Cited by 181
Research works printed but not linked: 2
- Elliott, R.: Stochastic calculus and its applications. New York: Springer 1982
- Wignarajah, G.: Complexity tests for statistical independence. M.S. thesis, University of Toledo, 1985
Cited by
Rukhin, A., Sota, J., Nechvatal, J., Smid, M., Barker, E., Leigh, S., Levenson, M., Vangel, M., Banks, D., Heckert, A., et al. (2000) · doi:10.6028/nist.sp.800-22 · Cited by 1,867
Probability Distributions on Cladograms
Aldous, D. (1996) · The IMA volumes in mathematics and its applications · doi:10.1007/978-1-4612-0719-1_1 · Cited by 216
Self-citationAsymptotic behavior of the Lempel-Ziv parsing scheme and digital search trees
Jacquet, P., & Szpankowski, W. (1995) · Theoretical Computer Science · doi:10.1016/0304-3975(94)00298-w · Cited by 106
Average redundancy rate of the Lempel-Ziv code
Louchard, G., & Szpankowski, W. (1997) · IEEE Transactions on Information Theory · doi:10.1109/18.567640 · Cited by 92
On the entropy of DNA: algorithms and measurements based on memory and rapid convergence
Farach-Colton, M., Noordewier, M. O., Savari, S. A., Shepp, L. A., Wyner, A. J., & Ziv, J. (1995) · doi:10.5555/313651.313662 · Cited by 81
Metadata
- Authors
- Aldous, D., & Shields, P.
- Affiliations
- University of California, Berkeley (US)
- University of Toledo (US)
- ORCID
- Aldous, David
- Venue
- Probability Theory and Related Fields
- Published
- 1988-11
- Volume
- 79
- Issue
- 4
- Pages
- 509-542
- ISSN
- 0178-8051 (ISSN-L)
- 1432-2064
- OpenAlex
- W2052638374
- Cited by
- 78
- References
- 21
- Citations by year
- 2026: 2 · 2024: 1 · 2023: 2 · 2022: 2 · 2020: 2 · 2018: 1 · 2017: 2 · 2016: 2 · 2015: 1 · 2014: 3 · 2012: 2
- FWCI
- 2.01
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- www.springer.com/tdm (tdm)
- www.springer.com/tdm (vor)
- Locations
- Probability Theory and Related Fields (publishedVersion)
- eScholarship (California Digital Library) (submittedVersion)
- Funders
- National Science Foundation
- Magyar Tudományos Akadémia
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Keywords
- random binary trees, diffusion limit, strong law of large numbers, central limit theorem, tree height distribution, asymptotic normality, entropy estimation, maximum tree height
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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.
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- CoChat. (2026). Citation check: A diffusion limit for a class of randomly-growing binary trees. https://app.cochat.ai/papers/10.1007/bf00318784
- The paper
- Aldous, D., & Shields, P. (1988). A diffusion limit for a class of randomly-growing binary trees. Probability Theory and Related Fields. https://doi.org/10.1007/bf00318784
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.
