Asymptotic geometric analysis: achievements and perspective
From MaRDI portal
Publication:6608541
DOI10.1007/978-3-031-26300-2_1MaRDI QIDQ6608541
Publication date: 20 September 2024
Convexity of real functions of several variables, generalizations (26B25) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Asymptotic theory of convex bodies (52A23) Asymptotic theory of Banach spaces (46B06)
Cites Work
- On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)
- Valuations and Euler-Type Relations on Certain Classes of Convex Polytopes
- Crofton formulas in projective Finsler spaces
- Random walks and anO*(n5) volume algorithm for convex bodies
- The Expected Norm of Random Matrices
- Equlibrium measure of a product subset of ℂⁿ
- Sample Covariance Matrices of Heavy-Tailed Distributions
- Some estimates of norms of random matrices
- Coverings by convex bodies and inscribed balls
- On the $L_{p}$-Minkowski problem
- A short proof of Hadwiger's characterization theorem
- Simple valuations on convex bodies
- Smallest singular value of sparse random matrices
- A Remark on Vertex Index of the Convex Bodies
- The logarithmic Minkowski problem
- Metric and isoperimetric problems in symplectic geometry
- Flag approximability of convex bodies and volume growth of Hilbert geometries
- On the geometry of polytopes generated by heavy-tailed random vectors
- Local 𝐿^{𝑝}-Brunn–Minkowski inequalities for 𝑝<1
- On mixed Hodge–Riemann relations for translation-invariant valuations and Aleksandrov–Fenchel inequalities
- Random polytopes obtained by matrices with heavy-tailed entries
- Reciprocals and Flowers in Convexity
- Novel view on classical convexity theory
- New Structures on Valuations and Applications
- Quantitative Version of a Silverstein’s Result
- Asymptotic Geometric Analysis, Part I
- On the spectral norm of Gaussian random matrices
- Asymptotic volume on Hilbert geometries
- Dual spheres have the same girth
- $p$-Means of Convex Bodies.
- Rapid Steiner Symmetrization of Most of a Convex Body and the Slicing Problem
- On the Volume of Tubes
- A Solution of the "Plank Problem"
- The Slicing Problem by Bourgain
- Remarks on symplectic capacities of p-products
- On subspaces contained in subsets of finite homogeneous spaces
- Description of translation invariant valuations on convex sets with solution of P. McMullen's conjecture
- A zoo of dualities
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Real-valued valuations on Sobolev spaces
- Sharp nonasymptotic bounds on the norm of random matrices with independent entries
- The lower tail of random quadratic forms with applications to ordinary least squares
- Covariance estimation for distributions with \({2+\varepsilon}\) moments
- On the expectation of the norm of random matrices with non-identically distributed entries
- On generic chaining and the smallest singular value of random matrices with heavy tails
- The log-Brunn-Minkowski inequality
- On higher order isotropy conditions and lower bounds for sparse quadratic forms
- Random approximation and the vertex index of convex bodies
- Hidden structures in the class of convex functions and a new duality transform
- On the weak limit of the largest eigenvalue of a large dimensional sample covariance matrix
- Fisher information and matrix-valued valuations
- Limit of the smallest eigenvalue of a large dimensional sample covariance matrix
- The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
- How close is the sample covariance matrix to the actual covariance matrix?
- Spectral norm of products of random and deterministic matrices
- From symplectic measurements to the Mahler conjecture
- On Hodge-Riemann relations for translation-invariant valuations
- The Weyl principle on the Finsler frontier
- The number of faces of centrally-symmetric polytopes
- On convex perturbations with a bounded isotropic constant
- Valuations on manifolds and Rumin cohomology
- Valuations with Crofton formula and Finsler geometry
- Convolution of convex valuations
- The plank problem for symmetric bodies
- A new duality transform
- A universality result for the smallest eigenvalues of certain sample covariance matrices
- On the role of convexity in isoperimetry, spectral gap and concentration
- The Brunn-Minkowski inequality in Gauss space
- The approximation of convex sets by polyhedra
- Extremal properties of half-spaces for spherically invariant measures
- Some conjectures on intrinsic volumes of Riemannian manifolds and Alexandrov spaces
- Coverings of random ellipsoids, and invertibility of matrices with i.i.d. heavy-tailed entries
- The dimension-free structure of nonhomogeneous random matrices
- Isotropic constants and Mahler volumes
- Sharp systolic inequalities for Reeb flows on the three-sphere
- Approximating a convex body by a polytope using the epsilon-net theorem
- Hard Lefschetz theorem for valuations, complex integral geometry, and unitarily invariant valuations.
- Flag numbers and floating bodies
- Random spaces generated by vertices of the cube
- Generalizations of the Busemann-Petty problem for sections of convex bodies
- Isoperimetric problems for convex bodies and a localization lemma
- The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
- An extension of Schäffer's dual girth conjecture to Grassmannians
- An almost constant lower bound of the isoperimetric coefficient in the KLS conjecture
- The smallest singular value of inhomogeneous square random matrices
- A Rockafellar-type theorem for non-traditional costs
- Log concavity and concentration of Lipschitz functions on the Boolean hypercube
- Bourgain's slicing problem and KLS isoperimetry up to polylog
- Examples around the strong Viterbo conjecture
- Kotrbatý's theorem on valuations and geometric inequalities for convex bodies
- Curvature measures of pseudo-Riemannian manifolds
- The Hadwiger theorem on convex functions. III: Steiner formulas and mixed Monge-Ampère measures
- The \(L_p\)-Brunn-Minkowski inequality for \(p<1\)
- A homogeneous decomposition theorem for valuations on convex functions
- Metric entropy of some classes of sets with differentiable boundaries
- Contact integral geometry and the Heisenberg algebra
- Bang's problem and symplectic invariants
- Valuations on convex functions and convex sets and Monge-Ampère operators
- Volume entropy of Hilbert metrics and length spectrum of Hitchin representations into \(\mathrm{PSL}(3,\mathbb{R})\)
- Inverse Littlewood-Offord theorems and the condition number of random discrete matrices
- The concept of duality in convex analysis, and the characterization of the Legendre transform
- Differential analysis of polarity: polar Hamilton-Jacobi, conservation laws, and Monge Ampère equations
- On the symplectic size of convex polytopes
- The M-ellipsoid, symplectic capacities and volume
- On the singular values of random matrices
- Integral geometry of complex space forms
- Theory of valuations on manifolds: A survey
- The Littlewood-Offord problem and invertibility of random matrices
- Smallest singular value of random matrices and geometry of random polytopes
- Lower bounds on the smallest eigenvalue of a sample covariance matrix.
- The asymptotics of ECH capacities
- On the interval of fluctuation of the singular values of random matrices
- Polar correspondence with respect to a convex region
- Uniqueness of curvature measures in pseudo-Riemannian geometry
- Optimal measure transportation with respect to non-traditional costs
- On the local systolic optimality of Zoll contact forms
- From harmonic analysis of translation-invariant valuations to geometric inequalities for convex bodies
- Elementary approach to closed billiard trajectories in asymmetric normed spaces
- Valuations on Sobolev spaces
- Valuations on Lp-Spaces
- Approximately gaussian marginals and the hyperplane conjecture
- On the limiting empirical measure of eigenvalues of the sum of rank one matrices with log-concave distribution
- Thrifty Approximations of Convex Bodies by Polytopes
- Fine approximation of convex bodies by polytopes
- Asymptotic Geometric Analysis, Part II
- Bounding the Smallest Singular Value of a Random Matrix Without Concentration
- Singular values of Gaussian matrices and permanent estimators
- A Brunn-Minkowski Inequality for Symplectic Capacities of Convex Domains
- RANDOM MATRICES: THE CIRCULAR LAW
- Kahane-Khinchin type averages
- Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles
- Smallest singular value of a random rectangular matrix
- On High Dimensional Maximal Functions Associated to Convex Bodies
- Random Fourier Series with Applications to Harmonic Analysis. (AM-101)
This page was built for publication: Asymptotic geometric analysis: achievements and perspective