Related papers: Assumptions of Randomness in Cosmology Models
Quel est, ou pourrait \^etre, la topologie globale de la partie spatiale de l'Univers ? L'Univers entier (pr\'ecis\'ement, l'hypersurface spatiale de celui-ci) est-il observable ? Les math\'ematiciens, les physiciens et les cosmologistes…
Extracting predictions from cosmological theories that describe a multiverse, for what we are likely to observe in our domain, is crucial to establishing the validity of these theories. One way to extract such predictions is from…
``Constants of Nature'' and cosmological parameters may in fact be variables related to some slowly-varying fields. In models of eternal inflation, such fields will take different values in different parts of the universe. Here I show how…
In this paper, we address the problem of constructing a uniform probability measure on $\mathbb{N}$. Of course, this is not possible within the bounds of the Kolmogorov axioms and we have to violate at least one axiom. We define a…
Astrophysical and cosmological signals such as the cosmic microwave background radiation, as observed, typically contain contributions of different components, and their statistical properties can be used to distinguish one from the other.…
To estimate cosmological parameters from a given dataset, we need to construct a likelihood function, which sometimes has a complicated functional form. We introduce the copula, a mathematical tool to construct an arbitrary multivariate…
Geometry constrains but does not dictate the topology of the 3--dimensional space. In a locally spatially homogeneous and isotropic universe, however, the topology of its spatial section dictates its geometry. We show that, besides…
The structure of the coincidence symmetry group of an arbitrary $n$-dimensional lattice in the $n$-dimensional Euclidean space is considered by describing a set of generators. Particular attention is given to the coincidence isometry…
Randomness extraction is the process of constructing a source of randomness of high quality from one or several sources of randomness of lower quality. The problem can be modeled using probability distributions and min-entropy to measure…
This paper develops a geometric reinterpretation of probability in which expectation arises from averaging in probability coordinates rather than in value space. By interpreting the cumulative distribution functions as coordinate maps, a…
The estimation of cosmological parameters from a given data set requires a construction of a likelihood function which, in general, has a complicated functional form. We adopt a Gaussian copula and constructed a copula likelihood function…
This paper studies when a sequence of probability measures on a metric space admit subsequential weak limits. A sufficient condition called sequential tightness is formulated, which relaxes some assumptions for asymptotic tightness used in…
Spherical manifolds yield cosmic spaces with positive curvature. They result by closing pieces from the sphere used by Einstein for his initial cosmology. Harmonic analysis on the manifolds aims at explaining the observed low amplitudes at…
Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to…
The Cosmic Defect theory has been confronted with four observational constraints: primordial nuclear species abundances emerging from the big bang nucleosynthesis; large scale structure formation in the universe; cosmic microwave background…
Building robust, interpretable, and secure AI system requires quantifying and representing uncertainty under a probabilistic perspective to mimic human cognitive abilities. However, probabilistic computation presents significant challenges…
The volume of data that will be produced by the next generation of astrophysical instruments represents a significant opportunity for making unplanned and unexpected discoveries. Conversely, finding unexpected objects or phenomena within…
The field of algorithmic randomness studies what it means for infinite binary sequences to be random for some given uncertainty model. Classically, martingale-theoretic notions of such randomness involve precise uncertainty models, and it…
Advantages of inhomogeneous cosmological models that are exact solutions of Einstein's equations over linearised perturbations of homogeneous models are presented. Examples of effects that can be described in the inhomogeneous ones are…
The pair separations statistical methods devised to detect the topology of the universe rely on the accurate knowledge of the three-dimensional positions of the cosmic sources. The determination of these positions, however, involves…