Related papers: On the relationship between mean observations, spa…
Consistency relations of large-scale structures provide exact nonperturbative results for cross-correlations of cosmic fields in the squeezed limit. They only depend on the equivalence principle and the assumption of Gaussian initial…
The possibility of obtaining symbolic expressions for cosmic backreaction is explored through a case study of so-called 2-region models. By using the publicly available symbolic regression algorithm AI Feynman, it is shown that the…
Bures distance holds a special place among various distance measures due to its several distinguished features and finds applications in diverse problems in quantum information theory. It is related to fidelity and, among other things, it…
The Sliced-Wasserstein distance (SW) is being increasingly used in machine learning applications as an alternative to the Wasserstein distance and offers significant computational and statistical benefits. Since it is defined as an…
We study the mean-field limit of the Atlas model and its connection to SDEs with dependence on the distribution of hitting and local times. The Atlas model describes a system of Brownian particles on the real line, where only the lowest…
Previous literature on random matrix and network science has traditionally employed measures derived from nearest-neighbor level spacing distributions to characterize the eigenvalue statistics of random matrices. This approach, however,…
Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system. This invariance is powerful, but discrete GW is a nonconvex quadratic optimal transport…
A systematic investigation of the relationship between different redshift estimation schemes for more than 91000 quasars in the Sloan Digital Sky Survey (SDSS) Data Release 6 (DR6) is presented. The publicly available SDSS quasar redshifts…
Nearest neighbor cells in $R^d,d\in\mathbb{N}$, are used to define coefficients of divergence ($\phi$-divergences) between continuous multivariate samples. For large sample sizes, such distances are shown to be asymptotically normal with a…
It is a common assumption amongst astronomers that, in the determination of the distances of remote sources from their apparent brightness, the cumulative gravitational lensing due to the matter in all the galaxies is the same, on average,…
We study pathwise approximation of scalar stochastic differential equations at a single time point or globally in time by means of methods that are based on finitely many observations of the driving Brownian motion. We prove lower error…
We reformulate the averaged Einstein equations in a form suitable for use with Newtonian gauge linear perturbation theory and track the size of the modifications to standard Robertson-Walker evolution on the largest scales as a function of…
In order to find a way to have a better formulation for numerical evolution of the Einstein equations, we study the propagation equations of the constraints based on the Arnowitt-Deser-Misner formulation. By adjusting constraint terms in…
The redshift drift is a small, dynamic change in the redshift of objects following the Hubble flow. Its measurement provides a direct, real-time, model-independent mapping of the expansion rate of the Universe. It is fundamentally different…
We study a modified mean-field approximation for the Ising Model in arbitrary dimension. Instead of taking a "central" spin, or a small "drop" of fluctuating spins coupled to the effective field of their nearest neighbors as in the…
Kaiser redshift-space distortion formula describes well the clustering of galaxies in redshift surveys on small scales, but there are numerous additional terms that arise on large scales. Some of these terms can be described using Newtonian…
Smoothing over structures in general relativity leads to a renormalisation of the background, and potentially many other effects which are poorly understood. Observables such as the distance-redshift relation when averaged on the sky do not…
Scatter in distance indicators introduces two conceptually distinct systematic biases when reconstructing peculiar velocity fields from redshifts and distances. The first is distance Malmquist bias (dMB) that affects individual distance…
We provide a general steady-state diffusion approximation result which bounds the Wasserstein distance between the reversible measure $\mu$ of a diffusion process and the measure $\nu$ of an approximating Markov chain. Our result is…
Properties of Random Overlap Structures (ROSt)'s constructed from the Edwards-Anderson (EA) Spin Glass model on $\Z^d$ with periodic boundary conditions are studied. ROSt's are $\N\times\N$ random matrices whose entries are the overlaps of…