Keyword

random polytopes

Description: Random geometric objects formed as convex hulls of sampled points, studied in probability, convex geometry, and stochastic geometry.

Primary topic: Point processes and geometric inequalities (80%)

Wikidata ID: wiki/Q114243499

OpenAlex ID: keywords/random-polytopes

Stochastic Geometry and Its Applications.

1988 · David Aldous, D. Stoyan, et al. · Journal of the American Statistical Association · 1,159

Random Subdivisions of Space into Crystals

1962 · E. N. Gilbert · The Annals of Mathematical Statistics · 391

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�ber die konvexe H�lle von n zuf�llig gew�hlten Punkten

1963 · A. R�nyi, R. Sulanke · Probability Theory and Related Fields · 348

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Random growth in a tessellation

1973 · Daniel Richardson · Mathematical Proceedings of the Cambridge Philosophical Society · 322

Integral Geometry and Geometric Probability

2004 · Luis A. Santaló, Mark Kac · Cambridge University Press eBooks · 281

Geometric Probability

1978 · Herbert Solomon · Society for Industrial and Applied Mathematics eBooks · 259

Smallest singular value of random matrices and geometry of random polytopes

2004 · A.E. Litvak, A. Pajor, et al. · Advances in Mathematics · 246

Proof of Poincaré’s geometric theorem

1913 · George D. Birkhoff · Transactions of the American Mathematical Society · 211

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Reconstruction and Subgaussian Operators in Asymptotic Geometric Analysis

2007 · Shahar Mendelson, Alain Pajor, et al. · Geometric and Functional Analysis · 200

Stereological methods, vol. 2: Theoretical foundations

1984 · George W.C. Hung · Microchemical Journal · 176

Convex bodies, economic cap coverings, random polytopes

1988 · I. Bárány, D. G. Larman · Mathematika · 159

The central limit problem for convex bodies

2003 · Milla Anttila, Keith Ball, et al. · Transactions of the American Mathematical Society · 144

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�ber die konvexe H�lle von n zuf�llig gew�hlten Punkten. II

1964 · A. R�nyi, R. Sulanke · Probability Theory and Related Fields · 140

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Offbeat Integral Geometry

1980 · Lawrence Zalcman · American Mathematical Monthly · 116

Instance-optimality in probability with an ℓ1 -minimization decoder

2009 · Ronald DeVore, Guergana Petrova, et al. · Applied and Computational Harmonic Analysis · 112

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Random coverings in several dimensions

1986 · Svante Janson · Acta Mathematica · 101

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Stochastische Geometrie

2000 · Rolf Schneider, Wolfgang Weil · Teubner-Skripten zur mathematischen Stochastik · 97

New Perspectives in Stochastic Geometry

2011 · Sreenivasan Ravi · Journal of the Royal Statistical Society Series A (Statistics in Society) · 95

On the mean value of the volume of a random polytope in a convex set

1974 · H. Groemer · Archiv der Mathematik · 92

Central limit theorems for random polytopes

2005 · Matthias Reitzner · Probability Theory and Related Fields · 88

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Intrinsic volumes andf-vectors of random polytopes

1989 · Imre Bárány · Mathematische Annalen · 82

Random polytopes and the Efron--Stein jackknife inequality

2003 · Matthias Reitzner · The Annals of Probability · 76

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Alternative model of random surfaces

1992 · R.V. Ambartzumian, G.K. Savvidy, et al. · Physics Letters B · 76

New Perspectives in Stochastic Geometry

2009 · Wilfried S. Kendall, Günter Last, et al. · Oberwolfach Reports · 74

Random points and lattice points in convex bodies

2008 · Imre Bárány · Bulletin of the American Mathematical Society · 70

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Works count: 751

Citation count: 10,510