211 citations · 985 across the 36 of their papers we have counts for
27 papers · 1 filter
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…
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…
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…
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 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…
Comparison Theorems for Gibbs Measures
Patrick Rebeschini, Ramon van Handel
The Dobrushin comparison theorem is a powerful tool to bound the difference between the marginals of high-dimensional probability distributions in terms of their local specificatio…
Ergodicity, Decisions, and Partial Information
Ramon van Handel
In the simplest sequential decision problem for an ergodic stochastic process X, at each time n a decision u_n is made as a function of past observations X_0,...,X_{n-1}, and a los…
Conditional ergodicity in infinite dimension
Xin Thomson Tong, Ramon van Handel
The goal of this paper is to develop a general method to establish conditional ergodicity of infinite-dimensional Markov chains. Given a Markov chain in a product space, we aim to…
Constructing Sublinear Expectations on Path Space
Marcel Nutz, Ramon van Handel
We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G-expectation of a Borel-me…
Ergodicity and stability of the conditional distributions of nondegenerate Markov chains
Xin Thomson Tong, Ramon van Handel
We consider a bivariate stationary Markov chain in a Polish state space, where only the process is presumed to be observable. The goal of this p…
The universal Glivenko-Cantelli property
Ramon van Handel
Let F be a separable uniformly bounded family of measurable functions on a standard measurable space, and let N_{[]}(F,ε,μ) be the smallest number of ε-brackets in L^1(μ) needed to…
On the exchange of intersection and supremum of sigma-fields in filtering theory
Ramon van Handel
We construct a stationary Markov process with trivial tail sigma-field and a nondegenerate observation process such that the corresponding nonlinear filtering process is not unique…