Related papers: Concentration of Haar measures, with an applicatio…
Large unweighted directed graphs are commonly used to capture relations between entities. A fundamental problem in the analysis of such networks is to properly define the similarity or dissimilarity between any two vertices. Despite the…
We consider random matrix ensembles on the set of Hermitian matrices that are heavy tailed, in particular not all moments exist, and that are invariant under the conjugate action of the unitary group. The latter property entails that the…
Ensembles of complex symmetric, and complex self dual random matrices are known to exhibit local statistical properties distinct from those of the non-Hermitian Ginibre ensembles. On the other hand, in distinction to the latter, the joint…
We consider non-Hermitian random matrices $X \in \mathbb{C}^{n \times n}$ with general decaying correlations between their entries. For large $n$, the empirical spectral distribution is well approximated by a deterministic density,…
We explore a method introduced by Chatterjee and Ledoux in a paper on eigenvalues of principle submatrices. The method provides a tool to prove concentration of measure in cases where there is a Markov chain meeting certain conditions, and…
Matrix concentration inequalities and their recently discovered sharp counterparts provide powerful tools to bound the spectrum of random matrices whose entries are linear functions of independent random variables. However, in many…
From concentration inequalities for the suprema of Gaussian or Rademacher processes an inequality is derived. It is applied to sharpen existing and to derive novel bounds on the empirical Rademacher complexities of unit balls in various…
The rate of convergence of simple random walk on the Heisenberg group over $Z/nZ$ with a standard generating set was determined by Bump et al [1,2]. We extend this result to random walks on the same groups with an arbitrary minimal…
We study moments of characteristic polynomials of truncated Haar distributed matrices from the three classical compact groups O(N), U(N) and Sp(2N). For finite matrix size we calculate the moments in terms of hypergeometric functions of…
We discuss a natural extension of Gilles Pisier's approach to the study of measure concentration, isoperimetry and Poincar\'e-type inequalities. This approach allows one to explore counterparts of various results about Gaussian measure in…
A comparison technique for finite random walks on finite graphs is introduced, using the well-known interlacing method. It yields improved return probability bounds. A key feature is the incorporation of parts of the spectrum of the…
In this paper, we study moment and concentration inequalities for the spectral norm of sums of dependent random matrices. We establish novel Rosenthal-Burkholder inequalities for discrete-time matrix local martingales,…
We discuss a method to estimate the measure of a compact set which is approximated using the Hausdorff distance by a sequence of compact sets. We do this by considering corresponding fattenings of the sequence of compact sets and showing…
We develop a rounding method based on random walks in polytopes, which leads to improved approximation algorithms and integrality gaps for several assignment problems that arise in resource allocation and scheduling. In particular, it…
A general method for obtaining moment inequalities for functions of independent random variables is presented. It is a generalization of the entropy method which has been used to derive concentration inequalities for such functions…
We establish conditions on sequences of graphs which ensure that the mixing times of the random walks on the graphs in the sequence converge. The main assumption is that the graphs, associated measures and heat kernels converge in a…
We obtain moment and Gaussian bounds for general Lipschitz functions evaluated along the sample path of a Markov chain. We treat Markov chains on general (possibly unbounded) state spaces via a coupling method. If the first moment of the…
We study the distribution of entries of a random permutation matrix under a "randomized basis," i.e., we conjugate the random permutation matrix by an independent random orthogonal matrix drawn from Haar measure. It is shown that under…
We study the distribution of the number of (non-backtracking) periodic walks on large regular graphs. We propose a formula for the ratio between the variance of the number of $t$-periodic walks and its mean, when the cardinality of the…
As random operations for quantum systems are intensively used in various quantum information tasks, a trustworthy measure of the randomness in quantum operations is highly demanded. The Haar measure of randomness is a useful tool with wide…