The DOI matches its Crossref record; 15 of the 15 references it cites were found in a registry or an index.
Concentration of measure and isoperimetric inequalities in product spaces
Open accessAbstract
The concentration of measure phenomenon in product spaces roughly states that, if a set A in a product Ω N of probability spaces has measure at least one half, “most” of the points of Ω n are “close” to A. We proceed to a systematic exploration of this phenomenon. The meaning of the word “most” is made rigorous by isoperimetrictype inequalities that bound the measure of the exceptional sets. The meaning of the work “close” is defined in three main ways, each of them giving rise to related, but different inequalities. The inequalities are all proved through a common scheme of proof. Remarkably, this simple approach not only yields qualitatively optimal results, but, in many cases, captures near optimal numerical constants. A large number of applications are given, in particular to Percolation, Geometric Probability, Probability in Banach Spaces, to demonstrate in concrete situations the extremely wide range of application of the abstract tools.
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
Probability Inequalities for sums of Bounded Random Variables
Hoeffding, W. (1994) · Springer Series in Statistics · doi:10.1007/978-1-4612-0865-5_26 · Cited by 6,666
Probability Inequalities for Sums of Bounded Random Variables
Hoeffding, W. (1963) · Journal of the American Statistical Association · doi:10.1080/01621459.1963.10500830 · Cited by 4,852
Spencer, J. (1991) · Medical Entomology and Zoology · Cited by 4,310
On the method of bounded differences
McDiarmid, C. (1989) · Surveys in Combinatorics, 1989 · doi:10.1017/cbo9781107359949.008 · Cited by 1,425
(1976) · Lecture Notes in Mathematics · doi:10.1007/bfb0082336 · Cited by 1,297
Ledoux, M., & Talagrand, M. (1991) · doi:10.1007/978-3-642-20212-4 · Cited by 1,160
Self-citationAsymptotic Theory of Finite Dimensional Normed Spaces
(1986) · Lecture Notes in Mathematics · doi:10.1007/bfb0075912 · Cited by 778
A Topological Application of the Isoperimetric Inequality
Gromov, M., & Milman, V. D. (1983) · American Journal of Mathematics · doi:10.2307/2374298 · Cited by 361
The chromatic number of random graphs
Bollobás, B. (1988) · Combinatorica · doi:10.1007/bf02122551 · Cited by 360
Poisson approximation for large deviations
Janson, S. (1990) · Random Structures & Algorithms · doi:10.1002/rsa.3240010209 · Cited by 207
Cited by
Concentration Inequalities: A Nonasymptotic Theory of Independence
Boucheron, S., Lugosi, G., & Massart, P. (2013) · doi:10.1093/acprof:oso/9780199535255.001.0001 · Cited by 1,768
On the geometry of metric measure spaces
Sturm, K.-T. (2006) · Acta Mathematica · doi:10.1007/s11511-006-0002-8 · Cited by 835
Concentration Inequalities and Model Selection
(2007) · Lecture Notes in Mathematics · doi:10.1007/978-3-540-48503-2 · Cited by 744
Frieze, A., & Karoński, M. (2015) · doi:10.1017/cbo9781316339831 · Cited by 576
A dynamic model of social network formation
Skyrms, B., & Pemantle, R. (2000) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.97.16.9340 · Cited by 553
Metadata
- Authors
- Talagrand, M.
- Venue
- Publications Mathématiques de l'IHÉS
- Publisher
- MathDoc/Centre Mersenne
- Published
- 1995-12-07
- Volume
- 81
- Pages
- 73-205
- ISSN
- 0073-8301 (ISSN-L)
- 1618-1913
- OpenAlex
- W1973286131
- Cited by
- 829
- References
- 15
- FWCI
- 36.38
- Type
- journal article
- Language
- en
- Open access
- green
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: Concentration of measure and isoperimetric inequalities in product spaces. https://app.cochat.ai/papers/10.1007/bf02699376
- The paper
- Talagrand, M. (1995). Concentration of measure and isoperimetric inequalities in product spaces. Publications Mathématiques de l'IHÉS. https://doi.org/10.1007/bf02699376
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.
