Related papers: Weak convergence implies convergence in mean withi…
The weak equivalence principle (WEP) is the cornerstone of gravitational theories. At the local scale, WEP has been tested to high accuracy by various experiments. On the intergalactic distance scale, WEP could be tested by comparing the…
Gaussian comparison inequalities provide a way of bounding probabilities relating to multivariate Gaussian random vectors in terms of probabilities of random variables with simpler correlation structures. In this paper, we establish the…
We analyze the convergence behavior of \emph{globally weakly} and \emph{locally strongly contracting} dynamics. Such dynamics naturally arise in the context of convex optimization problems with a unique minimizer. We show that convergence…
This article extends weak convergence bounds of Markov transition kernels to convergence bounds on the variance of the Markov kernel applied to Lipschitz functions. In the reversible case, weak convergence rates of the transition kernels…
For a sequence of uniformly bounded, degenerate semigroups on a Hilbert space, we compare various types of convergences to a limit semigroup. Among others, we show that convergence of the semigroups, or of the resolvents of the generators,…
We generalize finite-sample bounds for convex clustering to the setting where affinity weights appearing in the objective correspond to a general connected graph. These bounds and their analysis lead to a better understanding of clustering…
In this work we study the estimation of the density of a totally positive random vector. Total positivity of the distribution of a random vector implies a strong form of positive dependence between its coordinates and, in particular, it…
Let (G, X) be a transformation group where the group $G$ does not necessarily act freely on the space X. We investigate the extent to which the action of G may fail to be proper. Stability subgroups are used to define new notions of…
We offer an umbrella type result which extends weak convergence of the classical empirical process on the line to that of more general processes indexed by functions of bounded variation. This extension is not contingent on the type of…
Recently we proved (EPRSY, ERSTVY, ESY4, ESYY, EYY, EYY2, EYYrigi) that the eigenvalue correlation functions of a general class of random matrices converge, weakly with respect to the energy, to the corresponding ones of Gaussian matrices.…
Using the quantum transition path time probability distribution we show that time averaging of weak values leads to unexpected results. We prove a weak value time energy uncertainty principle and time energy commutation relation. We also…
The paper analyzes four classical signal-plus-noise models: the factor model, spiked sample covariance matrices, the sum of a Wigner matrix and a low-rank perturbation, and canonical correlation analysis with low-rank dependencies. The…
This paper investigates Frequentist consistency properties of the posterior distributions constructed via Generalized Variational Inference (GVI). A number of generic and novel strategies are given for proving consistency, relying on the…
Model-based clustering imposes a finite mixture modelling structure on data for clustering. Finite mixture models assume that the population is a convex combination of a finite number of densities, the distribution within each population is…
In this work we give a proof of the mean-field limit for $\lambda$-convex potentials using a purely variational viewpoint. Our approach is based on the observation that all evolution equations that we study can be written as gradient flows…
The formalism of weak measurement in quantum mechanics has revealed profound connections between measurement theory, quantum foundations, and signal processing. In this paper, we develop a pointer-free derivation of superoscillations,…
The power spectrum of weak lensing fluctuations has a non-Gaussian distribution due to its quadratic nature. On small scales the Central Limit Theorem acts to Gaussianize this distribution but non-Gaussianity in the signal due to…
Analysing the weak lensing distortions of the images of faint background galaxies provides a means to constrain the mass distribution of cluster galaxies and potentially to test the extent of their dark matter halos as a function of the…
General hypergeometric distribution (GHGD) definition: from a finite space $N$ containing $n$ elements, randomly select totally $T$ subsets $M_i$ (each contains $m_i$ elements, $1 \geq i \geq T$), what is the probability that exactly $x$…
In this paper, new results in random matrix theory are derived which allow us to construct a shrinkage estimator of the global minimum variance (GMV) portfolio when the shrinkage target is a random object. More specifically, the shrinkage…