12 pages, 2 figures, submitted to PNAS. Comments welcome!
We present efficient algorithms for computing the $N$-point correlation functions (NPCFs) of random fields in arbitrary $D$-dimensional homogeneous and isotropic spaces. Such statistics appear throughout the physical sciences, and provide a natural tool to describe a range of stochastic processes. Typically, NPCF estimators have $\mathcal{O}(n^N)$ complexity (for a data set containing $n$ particles); their application is thus computationally infeasible unless $N$ is small. By projecting onto a suitably-defined angular basis, we show that the estimators can be written in separable form, with complexity $\mathcal{O}(n^2)$, or $\mathcal{O}(n_{\rm g}\log n_{\rm g})$ if evaluated using a Fast Fourier Transform on a grid of size $n_{\rm g}$. Our decomposition is built upon the $D$-dimensional hyperspherical harmonics; these form a complete basis on the $(D-1)$-sphere and are intrinsically related to angular momentum operators. Concatenation of $(N-1)$ such harmonics gives states of definite combined angular momentum, forming a natural separable basis for the NPCF. In particular, isotropic correlation functions require only states with zero combined angular momentum. We provide explicit expressions for the NPCF estimators as applied to both discrete and gridded data, and discuss a number of applications within cosmology and fluid dynamics. The efficiency of such estimators will allow higher-order correlators to become a standard tool in the analysis of random fields.
16 pages (11 main body); 10 figures and 1 Table. Submitted to A&A. Comments welcome
Accepted for publication in ApJ. The 1D profile of DF2, in Fig. 4 and 5, shows an exponential decline at r> 35 arcsec (disk). Fig. 7 shows no signatures of tidal features in the outer parts of the galaxy
17 pages, 14 figures, Accepted for publication in MNRAS
15 pages, 13 figures, accepted for publication in AJ
Accepted for publication in MNRAS
15 pages, 10 figures. Submitted to A&A. Comments are welcome
6 pages, submitted to MNRAS
7 pages, 4 figures, MNRAS accepted
14 pages, Submitted to MNRAS
16 pages, 21 figures, 1 table
20 pages, 15 figures, submitted to ApJ, comments welcome
21 pages, 7 figures
9 pages, 9 figures
30 pages, 19 figures, to be published in ApJ
4 pages, 2 figures
10 pages, 7 figures
9 pages, 5 figures
7 pages, 4 figures, Accepted to the Planetary Science Journal
40 pages, 35 figures. Accepted for publication in ApJS. Data products available at: this https URL
Accepted for publication in ApJ
19 pages, 11 figures, accepted for publication in ApJ
6 pages, 3 figures, submitted to MNRAS
Accepted for publication in A&A
8 pages, 4 figures, invited talk at the conference Chemical elements in the Universe, a celebration of 150 years of the Periodic Table, December 2019, Bangalore, India
25 pages, 26 figures
32 pages, 22 figures
94 pages (20+74 pages in Supplementary), 6 figures (inc. fig.set 1 (19 images), fig.set 3 (21 images)), 14 tables (inc. 7 MRT), supplementary data archived on this https URL
11 pages, 7 figures. Accepted for publication in MNRAS
13 pages, 7 figures (in main text. 21 pages including appendices), accepted for publication in ApJ
25 pages, 13 figures (inc. 2 interactive figs, 1 interactive animation), 1 Table (inc. 6 MRT), submitted to ApJ, supplementary data (interactive figures, videos, machine readable tables) available on this https URL and archived on this https URL
Submitted to Icarus. Supplemental Material available at: this https URL (software), this https URL (animations)
To be published in The Astrophysical Journal Letters
12 pages, 11 figures, accepted by A&A
11 pages, 6 figures
7 pages, 3 figures
20 pages, 20 figures, accepted for publication in MNRAS
18 pages, 9 figures, submitted on 9th April 2021
Accepted by MNRAS
16 pages, 11 figure, Mg II QSO data are given. arXiv admin note: text overlap with arXiv:2105.12692
16 pages, 7 figures; accepted for publication in ApJ
25 pages, 11 figures. Submitted to ApJS
24 pages, 7 figures
26 pages, 11 figures
Conference paper presented at the 7th IAA Planetary Defense Conference, 26-30 April 2021, Vienna, Austria. IAA-PDC-21-11-37
Accepted for publication on A&A. The abstract has been shortened to fit the available space
This is the version of the article before peer review and submission. The published version is Kautsch, Veras, & Hansotia 2021, European Journal of Physics, 42, 035605, this https URL
7 pages, 4 figures
16 pages, 5 figures, accepted for publication in JGR: Space Physics
18 Pages, 8 Figures, Accepted in European Physical Journal C on 12.06.2021
8 pages, 4 figures
5 pages, no figures
1+15 pages, 4 figures
21 pages, 3 figures, accepted for publication in EPJC
Abstract is reduced due to arXiv limitations
22 pages, 9 figures; Invited review for Universe
28 pages,7 figures
30 pages, 7 figures
IEEE Transactions on Antennas and Propagation