On the geometry of polytopes generated by heavy-tailed random vectors

DOI10.1142/S0219199721500565zbMath1485.52005OpenAlexW3156096369MaRDI QIDQ5066318

Shahar Mendelson, Holger Rauhut, Olivier Guédon, Felix Krahmer, Christian Kümmerle

Publication date: 29 March 2022

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219199721500565

zbMATH Keywords

random matricesheavy tailssmall ball probabilityrandom polytopescompressed sensing\(\ell_1\)-quotient property

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Numerical optimization and variational techniques (65K10) Probabilistic methods in Banach space theory (46B09) Random matrices (algebraic aspects) (15B52) Random convex sets and integral geometry (aspects of convex geometry) (52A22) Asymptotic theory of convex bodies (52A23) Asymptotic theory of Banach spaces (46B06)

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Cites Work

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• A mathematical introduction to compressive sensing
• Sparse recovery under weak moment assumptions
• Probability in Banach spaces. Isoperimetry and processes
• Restricted isometry property of matrices with independent columns and neighborly polytopes by random sampling
• Instance-optimality in probability with an \(\ell _1\)-minimization decoder
• Asymptotic shape of a random polytope in a convex body
• Concentration of mass on convex bodies
• Convex measures on locally convex spaces
• Sharper bounds for Gaussian and empirical processes
• Sphere packing numbers for subsets of the Boolean \(n\)-cube with bounded Vapnik-Chervonenkis dimension
• Blaschke-Santaló inequalities
• A Bennett concentration inequality and its application to suprema of empirical processes
• Random spaces generated by vertices of the cube
• Stability and instance optimality for Gaussian measurements in compressed sensing
• Stability and robustness of \(\ell_1\)-minimizations with Weibull matrices and redundant dictionaries
• Smallest singular value of random matrices and geometry of random polytopes
• Learning without Concentration
• Suprema of Chaos Processes and the Restricted Isometry Property
• The Distribution of Rademacher Sums
• Learnability and the Vapnik-Chervonenkis dimension
• Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles
• EXTREMAL PROPERTIES OF ORTHOGONAL PARALLELEPIPEDS AND THEIR APPLICATIONS TO THE GEOMETRY OF BANACH SPACES
• The convex floating body.
• On the Gap Between Restricted Isometry Properties and Sparse Recovery Conditions
• Robustness to Unknown Error in Sparse Regularization
• Random polytopes obtained by matrices with heavy-tailed entries
• On the Geometry of Random Polytopes
• On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
• Compressed sensing
• New concentration inequalities in product spaces