Related papers: Introduction to Infinite Dimensional Statistics an…
A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the aproximation of the covariance when…
The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of…
Fundamental fields are a natural outcome in cosmology and particle physics and might therefore serve as a proxy for more complex interactions. The equivalence principle implies that all forms of matter gravitate, and one therefore expects…
This survey intends to cover recent approaches to black hole entropy which attempt to go beyond the standard semiclassical perspective. Quantum corrections to the semiclassical Bekenstein-Hawking area law for black hole entropy, obtained…
Using very long baseline interferometry, the Event Horizon Telescope (EHT) collaboration has resolved the shadows of two supermassive black holes. Model comparison is traditionally performed in image space, where imaging algorithms…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using the Taylor expansion, is…
We develop a formalism to analytically describe the clustering of matter in the mildly non-linear regime in the presence of massive neutrinos. Neutrinos, whose free streaming wavenumber ($k_{\rm fs}$) is typically longer than the non-linear…
Climate change poses significant challenges for accurate climate modeling due to the complexity and variability of non-Gaussian climate systems. To address the complexities of non-Gaussian systems in climate modeling, this thesis proposes a…
This is an introduction into the problem of how to set up black hole initial-data for the matter-free field equations of General Relativity. The approach is semi-pedagogical and addresses a more general audience of astrophysicists and…
We begin our journey by recalling the fundamentals of Probability Theory that underlie one of its most significant applications to real-world problems: Parametric Estimation. Throughout the text, we systematically develop this theme by…
We consider the recent description of elementary particles in terms of Quantum Mechanical Kerr-Newman Black Holes, a description which provides a rationale for and at the same time reconciles the Bohm-hydrodynamical formulation on the one…
These informal notes, initially prepared a few years ago, look at various questions related to infinite processes in several parts of mathematics, with emphasis on examples.
A light-front renormalization group analysis is applied to study matter which falls into massive black holes, and the related problem of matter with transplankian energies. One finds that the rate of matter spreading over the black hole's…
The sample covariance matrix of a random vector is a good estimate of the true covariance matrix if the sample size is much larger than the length of the vector. In high-dimensional problems, this condition is never met. As a result, in…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
The last three years have again seen new exciting developments in the area of higher dimensional black objects. For black objects with noncompact higher dimensions, the solution space was exlored further within the blackfold approach and…
This work is devoted to the study of some important questions in general relativity. They include topics related to astrophysical shock waves, impulsive signals, gravitational memory effect, black hole geometries and integrable systems…
In stochastic analysis, the flow of information through time is typically modelled using a filtration. We introduce some of the basic ideas involving enlargements of filtration. Here, we focus mainly on initial enlargements, where a given…
Because of physical assumptions and numerical approximations, low-order models are affected by uncertainties in the state and parameters, and by model biases. Model biases, also known as model errors or systematic errors, are difficult to…
We propose a method to account for model error due to unresolved scales in the context of the ensemble transform Kalman filter (ETKF). The approach extends to this class of algorithms the deterministic model error formulation recently…