Related papers: Subadditive Average Distances and Quantum Promptne…
Classical geometry can be described either in terms of a metric tensor $g_{ab}(x)$ or in terms of the geodesic distance $\sigma^2(x,x')$. Recent work, however, has shown that the geodesic distance is better suited to describe the quantum…
This work considers the asymptotic behavior of the distance between two sample covariance matrices (SCM). A general result is provided for a class of functionals that can be expressed as sums of traces of functions that are separately…
Mixed effect modeling for longitudinal data is challenging when the observed data are random objects, which are complex data taking values in a general metric space without linear structure. In such settings the classical additive error…
I introduce a family of closeness functions between causal Lorentzian geometries of finite volume and arbitrary underlying topology. When points are randomly scattered in a Lorentzian manifold, with uniform density according to the volume…
The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. In particular, it allows one to describe the classical Standard Model coupled to Euclidean gravity. However,…
The distance between a quantum state and its closest state not having a certain property has been used to quantify the amount of correlations corresponding to that property. This approach allows a unified view of the various kinds of…
The discrepant posterior phenomenon (DPP) is a counter-intuitive phenomenon that can frequently occur in a Bayesian analysis of multivariate parameters. It refers to the phenomenon that a parameter estimate based on a posterior is more…
Starting from the equations of motion in a 1 + 1 static, diagonal, Lorentzian spacetime, such as the Schwarzschild radial line element, I find another metric, but with Euclidean signature, which produces the same geodesics x(t). This…
Quantum coherence, rooted in the superposition principle of quantum mechanics, is a crucial quantum resource. Various measures, operational interpretations, and generalizations of quantum coherence have been proposed. In recent years, its…
The low energy effective action of gravity in any even dimension generally acquires non-local terms associated with the trace anomaly, generated by the quantum fluctuations of massless fields. The local auxiliary field description of this…
In a previous paper [gr-qc/0104001; Class. Quant. Grav. 18 (2001) 3595-3610] we have shown that the occurrence of curved spacetime ``effective Lorentzian geometries'' is a generic result of linearizing an arbitrary classical field theory…
The geodesic deviation equation (GDE) describes the tendency of objects to accelerate towards or away from each other due to spacetime curvature. The GDE assumes that nearby geodesics have a small rate of separation, which is formally…
In the Lorentz invariant formalism of compact space-time dimensions the assumption of periodic boundary conditions represents a consistent semi-classical quantization condition for relativistic fields. In [arXiv:0903.3680] we have shown,…
Consider the geodesic flow on a real-analytic closed hypersurface $M$ of $\mathbb{R}^n$, equipped with the standard Euclidean metric. The flow is entirely determined by the manifold and the Riemannian metric. Typically, geodesic flows are…
In pregeometry a metric arises as a composite object at large distances. We investigate if its signature, which distinguishes between time and space, could be a result of the dynamics rather than being built in already in the formulation of…
In this paper we investigate the Erd\"os/Falconer distance conjecture for a natural class of sets statistically, though not necessarily arithmetically, similar to a lattice. We prove a good upper bound for spherical means that have been…
Geodesic distance serves as a reliable means of measuring distance in nonlinear spaces, and such nonlinear manifolds are prevalent in the current multimodal learning. In these scenarios, some samples may exhibit high similarity, yet they…
We consider two disjoint sets of points. If at least one of the sets can be embedded into an Euclidean space, then we provide sufficient conditions for the two sets to be jointly embedded in one Euclidean space. In this joint Euclidean…
A geometric theory for spacetimes whose world lines associated with physical particles have an upper bound for the proper acceleration is developed. After some fundamental remarks on the requirements that the classical dynamics for point…
Some first results are presented regarding the behavior of invariant correlations in simplicial gravity, with an action containing both a bare cosmological term and a lattice higher derivative term. The determination of invariant…