Related papers: The total variation distance between high-dimensio…
The paper contains results in three areas: First we present a general estimate for tail probabilities of Gaussian quadratic forms with known expectation and variance. Thereafter we analyze the distribution of norms of complex Gaussian…
We study the problem of estimating the mean of a multivariatedistribution based on independent samples. The main result is the proof of existence of an estimator with a non-asymptotic sub-Gaussian performance for all distributions…
We conjecture that the current fluctuations in one-dimensional driven transport systems obey an upper bound determined by the mean current and the driving force. This inequality originates from repulsive interactions between transporting…
We present several refinements on the fluctuations of sequences of random vectors (with values in the Euclidean space $\mathbb{R}^d$) which converge after normalization to a multidimensional Gaussian distribution. More precisely we refine…
A lower bound for the interleaving distance on persistence vector spaces is given in terms of rank invariants. This offers an alternative proof of the stability of rank invariants.
Given a compact smooth boundaryless manifold with dimension greater than one endowed with a locally positive non-atomic measure $\mu$, we prove that typical $\mu$-preserving homeomorphisms have upper metric mean dimension, with respect to…
We present an extensive analysis of relative deviation bounds, including detailed proofs of two-sided inequalities and their implications. We also give detailed proofs of two-sided generalization bounds that hold in the general case of…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
Triviality and vacuum stability bounds on the Higgs and top quark masses in a rather general class of supersymmetric extensions of the Standard Model are compared with the corresponding bounds without supersymmetry. Due to generic…
We give exponential upper bounds for $P(S \le k)$, in particular $P(S=0)$, where $S$ is a sum of indicator random variables that are positively associated. These bounds allow, in particular, a comparison with the independent case. We give…
This article describes the various experimental bounds on the variation of the fundamental constants of nature. After a discussion on the role of fundamental constants, of their definition and link with metrology, the various constraints on…
We analyze the effect of a heterogeneous variance on bump detection in a Gaussian regression model. To this end we allow for a simultaneous bump in the variance and specify its impact on the difficulty to detect the null signal against a…
Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…
We provide an elementary proof of the lower bound for the variance of continuous unimodal distributions and obtain analogous bounds for the higher order central moments. A lower bound for the rth central moment of discrete distribution is…
Let C = C(l_1, ..., l_n) be the n-dimensional orthogonal cross-polytope whose axes are of length l_1,..., l_n. Subject to the condition \sum l_i^2 = 1, the mean width of C is minimised when l_i = 1/sqrt{n} for every i, and it is maximised…
We establish bounds on the KL divergence between two multivariate Gaussian distributions in terms of the Hamming distance between the edge sets of the corresponding graphical models. We show that the KL divergence is bounded below by a…
An upper bound for Zolotarev distances between probability measures on multidimensional Euclidean spaces is given in terms of similar distances between one dimensional projections.
We derive upper and lower bounds on the determinant of an exponential matrix. They can be transformed into corresponding bounds for the determinant of a univariate Gaussian matrix.
We propose three measures of mutual dependence between multiple random vectors. All the measures are zero if and only if the random vectors are mutually independent. The first measure generalizes distance covariance from pairwise dependence…
The gamma difference distribution is defined as the difference of two gamma distributions, with in general different shape and rate parameters. Starting with knowledge of the corresponding characteristic function, a second order linear…