Random Fields and Geometry
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
For many Gaussian random fields, it is possible to determine the distribution of the Euler characteristic of excursion sets in terms of certain parameters defining the random field.
“It turns out that for many Gaussian random fields, as shown by Adler and Taylor, it is possible to determine the distribution of the statistic given by the Euler characteristic of the excursion sets, in terms of certain parameters defining the random field.”
From Topological pattern recognition for point cloud data (2014) · cites this paper as Adler and Taylor (2007)
Cited by
Sorted by citations
Vector field statistical analysis of kinematic and force trajectories
Pataky, T. C., Robinson, M. A., & Vanrenterghem, J. (2013) · Journal of Biomechanics · doi:10.1016/j.jbiomech.2013.07.031 · Cited by 741 · see citing works
Pataky, T. C., Vanrenterghem, J., & Robinson, M. A. (2015) · Journal of Biomechanics · doi:10.1016/j.jbiomech.2015.02.051 · Cited by 385 · see citing works
Topological pattern recognition for point cloud data
Carlsson, G. (2014) · Acta Numerica · doi:10.1017/s0962492914000051 · Cited by 230 · see citing works
Pataky, T. C., Vanrenterghem, J., & Robinson, M. A. (2016) · Journal of Biomechanics · doi:10.1016/j.jbiomech.2016.03.032 · Cited by 187 · see citing works
Robinson, M. A., Vanrenterghem, J., & Pataky, T. C. (2015) · Journal of Electromyography and Kinesiology · doi:10.1016/j.jelekin.2014.10.018 · Cited by 127 · see citing works
Diophantine Gaussian excursions and random walks
Lachièze-Rey, R. (2021) · arXiv · doi:10.48550/arxiv.2104.07290 · Cited by 1 · see citing works
“ω[k],i = ω[1],i, it yields stationary random sets in R with any reasonable asymptotic prescribed variance behaviour.”
BackgroundInfluential
- Venue
- Springer Monographs in Mathematics
- Publisher
- Springer New York
- Published
- 2007
- ISSN
- 1439-7382 (ISSN-L)
- OpenAlex
- W4210854635
- Cited by
- 280
- References
- 0
- Citations by year
- 2026: 2 · 2025: 31 · 2024: 27 · 2023: 30 · 2022: 26 · 2021: 13 · 2020: 19 · 2019: 20 · 2018: 13 · 2017: 9 · 2016: 15 · 2015: 10 · 2014: 18 · 2013: 14 · 2012: 8
- FWCI
- 0.99
- Type
- book
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Springer monographs in mathematics (publishedVersion)
- Funders
- University of California, Santa Barbara
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Physical Sciences › Mathematics › Applied Mathematics › Point processes and geometric inequalities
- Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
- Keywords
- random fields, random geometry, stochastic geometry, random sets, random measures
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.
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