211 citations · 985 across the 36 of their papers we have counts for
38 papers
On the subgaussian comparison theorem
Ramon van Handel
The aim of this expository note is to prove that any -subgaussian random vector is dominated in the convex ordering by a universal constant times a standard Gaussian vector. Thi…
A new approach to strong convergence II. The classical ensembles
Chi-Fang Chen, Jorge Garza-Vargas, Ramon van Handel
The first paper in this series introduced a new approach to strong convergence of random matrices that is based primarily on soft arguments. This method was applied to achieve a re…
Matrix Concentration Inequalities and Free Probability II. Two-sided Bounds and Applications
Afonso S. Bandeira, Giorgio Cipolloni, Dominik Schröder +1
The first paper in this series introduced a new family of nonasymptotic matrix concentration inequalities that sharply capture the spectral properties of very general random matric…
A new approach to strong convergence
Chi-Fang Chen, Jorge Garza-Vargas, Joel A. Tropp +1
A family of random matrices is said to converge strongly to a family of bounded operators when $\|P(\bolds…
Extremal random matrices with independent entries and matrix superconcentration inequalities
Tatiana Brailovskaya, Ramon van Handel
We prove nonasymptotic matrix concentration inequalities for the spectral norm of (sub)gaussian random matrices with centered independent entries that capture fluctuations at the T…
The extremals of the Kahn-Saks inequality
Ramon van Handel, Alan Yan, Xinmeng Zeng
A classical result of Kahn and Saks states that given any partially ordered set with two distinguished elements, the number of linear extensions in which the ranks of the distingui…
A localization-delocalization transition for nonhomogeneous random matrices
Laura Shou, Ramon van Handel
We consider self-adjoint Gaussian random matrices defined by an arbitrary deterministic sparsity pattern with nonzero entries per row. We show that such random matr…
The local logarithmic Brunn-Minkowski inequality for zonoids
Ramon van Handel
The aim of this note is to show that the local form of the logarithmic Brunn-Minkowski conjecture holds for zonoids. The proof uses a variant of the Bochner method due to Shenfeld…
Universality and sharp matrix concentration inequalities
Tatiana Brailovskaya, Ramon van Handel
We show that, under mild assumptions, the spectrum of a sum of independent random matrices is close to that of the Gaussian random matrix whose entries have the same mean and covar…
Shephard's inequalities, Hodge-Riemann relations, and a conjecture of Fedotov
Ramon van Handel
A well-known family of determinantal inequalities for mixed volumes of convex bodies were derived by Shephard from the Alexandrov-Fenchel inequality. The classic monograph Geometri…
Matrix Concentration Inequalities and Free Probability
Afonso S. Bandeira, March T. Boedihardjo, Ramon van Handel
A central tool in the study of nonhomogeneous random matrices, the noncommutative Khintchine inequality, yields a nonasymptotic bound on the spectral norm of general Gaussian rando…
The Extremals of the Alexandrov-Fenchel Inequality for Convex Polytopes
Yair Shenfeld, Ramon van Handel
The Alexandrov-Fenchel inequality, a far-reaching generalization of the classical isoperimetric inequality to arbitrary mixed volumes, lies at the heart of convex geometry. The cha…
Rademacher type and Enflo type coincide
Paata Ivanisvili, Ramon van Handel, Alexander Volberg
A nonlinear analogue of the Rademacher type of a Banach space was introduced in classical work of Enflo. The key feature of Enflo type is that its definition uses only the metric s…
The Extremals of Minkowski's Quadratic Inequality
Yair Shenfeld, Ramon van Handel
In a seminal paper "Volumen und Oberfläche" (1903), Minkowski introduced the basic notion of mixed volumes and the corresponding inequalities that lie at the heart of convex geomet…
Mixed volumes and the Bochner method
Yair Shenfeld, Ramon van Handel
At the heart of convex geometry lies the observation that the volume of convex bodies behaves as a polynomial. Many geometric inequalities may be expressed in terms of the coeffici…
The dimension-free structure of nonhomogeneous random matrices
Rafał Latała, Ramon van Handel, Pierre Youssef
Let be a symmetric random matrix with independent but non-identically distributed centered Gaussian entries. We show that $$ \mathbf{E}\|X\|_{S_p} \asymp \mathbf{E}\Bigg[ \Bigg…
The equality cases of the Ehrhard-Borell inequality
Yair Shenfeld, Ramon van Handel
The Ehrhard-Borell inequality is a far-reaching refinement of the classical Brunn-Minkowski inequality that captures the sharp convexity and isoperimetric properties of Gaussian me…
Structured Random Matrices
Ramon van Handel
Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in th…
Chaining, Interpolation, and Convexity II: The contraction principle
Ramon van Handel
The generic chaining method provides a sharp description of the suprema of many random processes in terms of the geometry of their index sets. The chaining functionals that arise i…
The Borell-Ehrhard Game
Ramon van Handel
A precise description of the convexity of Gaussian measures is provided by sharp Brunn-Minkowski type inequalities due to Ehrhard and Borell. We show that these are manifestations…
Chaining, Interpolation, and Convexity
Ramon van Handel
We show that classical chaining bounds on the suprema of random processes in terms of entropy numbers can be systematically improved when the underlying set is convex: the entropy…
On the spectral norm of Gaussian random matrices
Ramon van Handel
Let be a symmetric random matrix with independent but non-identically distributed Gaussian entries. It has been conjectured by Latał{a} that the spectral norm of $X…
Sharp nonasymptotic bounds on the norm of random matrices with independent entries
Afonso S. Bandeira, Ramon van Handel
We obtain nonasymptotic bounds on the spectral norm of random matrices with independent entries that improve significantly on earlier results. If is the symmetric m…
Phase Transitions in Nonlinear Filtering
Patrick Rebeschini, Ramon van Handel
It has been established under very general conditions that the ergodic properties of Markov processes are inherited by their conditional distributions given partial information. Wh…