Related papers: Quantitative version of a Silverstein's result
Using proof-theoretic methods in the style of proof mining, we give novel computationally effective limit theorems for the convergence of the Cesaro-means of certain sequences of random variables. These results are intimately related to…
This paper deals with the scenario approach to robust optimization. This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in the parameters of an optimization problem. Solving the resulting…
We compute the survival probability of an initial state, with an energy in a certain window, by means of random matrix theory. We determine its probability distribution and show that is is universal, i.e. caracterised only by the symmetry…
Johnson-Lindenstrauss guarantees certain topological structure is preserved under random projections when project high dimensional deterministic vectors to low dimensional vectors. In this work, we try to understand how random matrix affect…
We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results…
The asymptotic behaviour of empirical measures has plenty of studies. However, the research on conditional empirical measures is limited. Being the development of Wang \cite{eW1}, under the quadratic Wasserstein distance, we investigate the…
We prove a version of a general transfer theorem for random sequences with independent random indexes in the double array limit setting under relaxed conditions. We also prove its partial inverse providing the necessary and sufficient…
In this brief paper the probability density of a random real, complex and quaternion determinant is rederived using singular values. The behaviour of suitably rescaled random determinants is studied in the limit of infinite order of the…
In this paper we prove exponential inequalities (also called Bernstein's inequality) for fractional martingales. As an immediate corollary, we will discuss weak law of large numbers for fractional martingales under divergence assumption on…
This thesis consists of two independent parts: random matrices, which form the first one-third of this thesis, and machine learning, which constitutes the remaining part. The main results of this thesis are as follows: a necessary and…
We provide a general theorem on the asymptotic behavior of stochastic processes that conform to a relaxed supermartingale condition. The distinguishing feature of our result is that it provides quantitative convergence guarantees at a much…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
We establish some deviation inequalities, moment bounds and almost sure results for the Wasserstein distance of order p $\in$ [1, $\infty$) between the empirical measure of independent and identically distributed R d-valued random variables…
In ordinary situations involving a small part of the universe, Born's rule seems to work well for calculating probabilities of observations in quantum theory. However, there are a number of reasons for believing that it is not adequate for…
A simple proof is given that the probabilities of observations in a large universe are not given directly by Born's rule as the expectation values of projection operators in a global quantum state of the entire universe. An alternative…
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
We study approximation in the unit interval by rational numbers whose numerators are selected randomly with certain probabilities. Previous work showed that an analogue of Khintchine's Theorem holds in a similar random model and raised the…
In this work we present (and encourage the use of) the Williamson theorem and its consequences in several contexts in physics. We demonstrate this theorem using only basic concepts of linear algebra and symplectic matrices. As an immediate…
The four moment theorem asserts, roughly speaking, that the joint distribution of a small number of eigenvalues of a Wigner random matrix (when measured at the scale of the mean eigenvalue spacing) depends only on the first four moments of…
We introduce a new class of large structured random matrices characterized by four fundamental properties which we discuss. We prove that this class is stable under matrix-valued and pointwise non-linear operations. We then formulate an…