Official NIST-hosted Chapter 10 slide deck. Slide 10.18, Curvature Check with Center Points, gives the contrast interval using center standard deviation; assumptions and F-statistic derivation are made explicit in the wiki. No individual author/date established.

By Sabyasachi Chatterjee, Adityanand Guntuboyina, Bodhisattva Sen.

Author-hosted preprint dated 13 November 2013, title as on this version. Introduction equations (5)–(6): isotonic LSE risk upper bound and flat-signal behavior; Section 4.1, Theorem 4.3: Gaussian local minimax lower bound around uniformly increasing sequences. Later versions use a different title; keep the cited-version identity.

By Art B. Owen.

Author companion site identifies the monograph, its nonparametric likelihood motivation and ISBN 1584880716. The normalization, constraint and two-point numerical calculation in the wiki are independent derivations; no inaccessible page locator is claimed.

Official SciPy reference. Notes: all concentration parameters positive, simplex support and multivariate beta normalization. Coordinate-measure qualification and K=3 numerical example independently derived.

Official SciPy user guide. Standardized density, CDF and quantile; restore the arbitrary positive scale. Tail-moment criterion and numerical example independently derived.

By C. M. Fortuin, P. W. Kasteleyn, J. Ginibre.

Communications in Mathematical Physics 22, 89–103. DOI: doi.org/10.1007/BF01651330 . Publisher abstract: positive association for increasing functions on finite distributive lattices under the mass convexity condition; applications to Ising and random-cluster models. Full PDF access was unavailable; no unverified theorem numbering is supplied.

By Stéphane Boucheron, Gábor Lugosi, Pascal Massart.

Electronic Journal of Probability 14, paper 64, 1884–1899. DOI: doi.org/10.1214/EJP.v14-690 . Definitions 1–3 and Theorem 1, especially the additional increment hypothesis in the third conclusion, printed p. 1887. The primary PDF contains a typographical Pacal in its byline; the established Pascal spelling also appears in its correspondence address and publisher book byline.

By Ramon van Handel.

Author-hosted lecture notes, version 21 December 2016. Section 3.4: Gaussian entropy and energy conventions; Theorem 4.8: T1 and concentration; Theorem 4.15: tensorization mechanism; Theorem 4.20 and Remark 4.25: global one-sided coordinate comparison and lower-tail variance proxy.

Proposition 1 states the Erdős-Turán inequality for a probability measure on the unit circle, with a universal constant and normalized arc length. The finite-point version follows by taking an empirical measure.

By Jerome H. Friedman, Trevor Hastie, Robert Tibshirani.

PDF: hastie.su.domains/Papers/graph.pdf

Biostatistics 9(3), 432–441; DOI: 10.1093/biostatistics/kxm045. Online 12 December 2007. Equations 2.1, 2.6 and Remark 2.2. Statistician Jerome H. Friedman verified by Stanford Statistics faculty listing; distinct from physicist Jerome Isaac Friedman.

By Tony Cai, Weidong Liu, Xi Luo.

PDF: arxiv.org/pdf/1102.2233

Section 2 defines entrywise objective, max-entry constraint, symmetric selection and column linear programs. Positive definiteness is a theorem under assumptions, not a program constraint.

By Vladimir Koltchinskii, Karim Lounici.

PDF: arxiv.org/pdf/1405.2468

Inspected v3, 1 July 2014. Definition 1, trace-rank discussion and Corollary 2, equation 2.8. Gaussian dimension (E||X||)^2/||Sigma|| is comparable to trace(Sigma)/||Sigma|| in Euclidean space.

By R. G. Edwards, A. D. Sokal.

Physical Review D 38, 2009–2012. Original four-page author-mirrored scan found on ResearchGate; scanned PDF has no machine-readable text. Joint-law derivation in wiki is explicit algebra.

By C. M. Fortuin, P. W. Kasteleyn.

Physica 57, 536–564. Leiden institutional publication record: www.lorentz.leidenuniv.nl/IL-publications/1972.html .

By Hugo Duminil-Copin, Vincent Tassion.

Inspected preprint 8 October 2015, arXiv:1502.03051; original title has Z^d. Theorem 1.1 and section 2.1.

By Michael Aizenman, Charles M. Newman.

Journal of Statistical Physics 36(1–2), 107–143. Author/institutional record collaborate.princeton.edu/en/publications/tree-graph-inequalities-and-critical-behavior-in-percolation-mode/ confirms diagrammatic convergence criterion for susceptibility exponent gamma=1.

By P. D. Seymour, D. J. A. Welsh.

Annals of Discrete Mathematics 3, 227–245; DOI: 10.1016/S0167-5060(08)70509-0. Sections 4–5 and Lemmas 5.2–5.4.

By Olivier Catoni.

PDF: arxiv.org/pdf/1009.2048

Preprint arXiv:1009.2048, submitted 10 September 2010, revised 12 August 2011. Section 2, equations 2.1–2.3 and Proposition 2.4. The inspected PDF has a regenerated 26 November 2024 header; this is not its original submission date.

Section6.1, printed pp.13–14 and Figure6.2, constructs the trivial bijection and recovers the original map from the vertex bipartition.

By Judea Pearl. Author-hosted supplement to Causality: bayes.cs.ucla.edu/BOOK-2K/d-sep.html

Sections1,1.2 and1.3 state the path criterion, blocking by conditioned noncolliders and activation by conditioning on a collider or its descendant.