# A stability theorem for bigraded persistence barcodes

arXiv: https://arxiv.org/abs/2303.14694 · HTML: https://mlsanity.com/paper/2303.14694/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 28 references that are in the map.
- First posted on arXiv 26 Mar 2023.

## Builds on (most cited first, 2 of 2)

- [Subsampling Methods for Persistent Homology](https://mlsanity.com/paper/1406.1901/) (2014)
- [From Geometry to Topology: Inverse Theorems for Distributed Persistence](https://mlsanity.com/paper/2101.12288/) (2021)

## Abstract (arXiv)

We define bigraded persistent homology modules and bigraded barcodes of a finite pseudo-metric space X using the ordinary and double homology of the moment-angle complex associated with the Vietoris-Rips filtration of X. We prove a stability theorem for the bigraded persistent double homology modules and barcodes.