# Hierarchical Clustering in LambdaCDM Cosmologies via Persistence Energy

arXiv: https://arxiv.org/abs/2401.01988 · HTML: https://mlsanity.com/paper/2401.01988/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 3 Jan 2024.

## Builds on (most cited first, 6 of 6)

- [The persistence landscape and some of its properties](https://mlsanity.com/paper/1810.04963/) (2018)
- [Understanding the Topology and the Geometry of the Space of Persistence Diagrams via Optimal Partial Transport](https://mlsanity.com/paper/1901.03048/) (2019)
- [Estimation and Quantization of Expected Persistence Diagrams](https://mlsanity.com/paper/2105.04852/) (2021)
- [Approximating Persistent Homology for Large Datasets](https://mlsanity.com/paper/2204.09155/) (2022)
- [Statistical learning on measures: an application to persistence diagrams](https://mlsanity.com/paper/2303.08456/) (2023)
- [Discrete transforms of quantized persistence diagrams](https://mlsanity.com/paper/2312.17093/) (2023)

## Abstract (arXiv)

In this research, we investigate the structural evolution of the cosmic web, employing advanced methodologies from Topological Data Analysis. Our approach involves leveraging LITE, an innovative method from recent literature that embeds persistence diagrams into elements of vector spaces. Utilizing this methodology, we analyze three quintessential cosmic structures: clusters, filaments, and voids. A central discovery is the correlation between textitPersistence Energy and redshift values, linking persistent homology with cosmic evolution and providing insights into the dynamics of cosmic structures.