Related papers: Assumptions of Randomness in Cosmology Models
Do completely unpredictable events exist in nature? Classical theory, being fully deterministic, completely excludes fundamental randomness. On the contrary, quantum theory allows for randomness within its axiomatic structure. Yet, the fact…
General relativity treats spacetime as dynamical and exhibits its breakdown at singularities. This failure is interpreted as evidence that quantum gravity is not a theory formulated within spacetime; instead, it must explain the very…
For a random matrix of entries sampled independently from a fairly general distribution in Z we study the probability that the cokernel is isomorphic to a given finite abelian group, or when it is cyclic. This includes the probability that…
The concept of a random Lagrangian is proposed. It is considered as a basis for a new view of the old problems such as renormalization, nonzero vacuum energy and the anthropic principle. It gives rise to nontrivial consequences both in…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
We make precise sense of the idea of "molecular chaos" through algorithmic randomness of microscopic trajectories, and ground macroscopic irreversibility in the lack of symmetry under time reversal of this property. This concept of…
Representation theory is shown to be incomplete in terms of enumerating all integrable limits of quantum systems. As a consequence, one can find exactly solvable Hamiltonians which have apparently strongly broken symmetry. The number of…
In the landscape, if there is to be any prospect of scientific prediction, it is crucial that there be states which are distinguished in some way. The obvious candidates are states which exhibit symmetries. Here we focus on states which…
We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common…
Recent observations suggest that the ratio of the total density to the critical density of the universe, $\Omega_0$, is likely to be very close to one, with a significant proportion of this energy being in the form of a dark component with…
We extend the notion of randomness (in the version introduced by Schnorr) to computable Probability Spaces and compare it to a dynamical notion of randomness: typicality. Roughly, a point is typical for some dynamic, if it follows the…
Algorithmic statistics studies explanations of observed data that are good in the algorithmic sense: an explanation should be simple i.e. should have small Kolmogorov complexity and capture all the algorithmically discoverable regularities…
Can you decide if there is a coincidence in the numbers counting two different combinatorial objects? For example, can you decide if two regions in $\mathbb{R}^3$ have the same number of domino tilings? There are two versions of the…
Spekkens has introduced an epistemically restricted classical theory of discrete systems, based on discrete phase space. The theory manifests a number of quantum-like properties but cannot fully imitate quantum theory because it is…
This work starts from definition of randomness, the results of algorithmic randomness are analyzed from the perspective of application. Then, the source and nature of randomness is explored, and the relationship between infinity and…
Harmonic slicing has in recent years become a standard way of prescribing the lapse function in numerical simulations of general relativity. However, as was first noticed by Alcubierre (1997), numerical solutions generated using this…
In this paper a relative number density parameter, called the neighborhood function, is introduced so that the crowded nature of the neighborhood of individual sources can be described. With this parameter one can determine the probability…
Bayesian model selection provides the cosmologist with an exacting tool to distinguish between competing models based purely on the data, via the Bayesian evidence. Previous methods to calculate this quantity either lacked general…
We introduce the concept of $\epsilon$-uncontrollability for random linear systems, i.e. linear system in which the usual matrices have been replaced by random matrices. We also estimate the $\epsilon$-uncontrollability in the case where…
This brief paper develops a probability density that models processes for which the physical mechanism is unknown. It has desirable properties which are not realized by densities derived from Gaussian process or other classic methods. In…