The infimal convolution structure of the Hellinger-Kantorovich distance
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913740514918400 |
|---|---|
| author | De Ponti, Nicolò Sodini, Giacomo Enrico Tamanini, Luca |
| author_facet | De Ponti, Nicolò Sodini, Giacomo Enrico Tamanini, Luca |
| contents | We show that the Hellinger-Kantorovich distance can be expressed as the metric infimal convolution of the Hellinger and the Wasserstein distances, as conjectured by Liero, Mielke, and Savaré. To prove it, we study with the tools of Unbalanced Optimal Transport the so called Marginal Entropy-Transport problem that arises as a single minimization step in the definition of infimal convolution. Careful estimates and results when the number of minimization steps diverges are also provided, both in the specific case of the Hellinger-Kantorovich setting and in the general one of abstract distances. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12939 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The infimal convolution structure of the Hellinger-Kantorovich distance De Ponti, Nicolò Sodini, Giacomo Enrico Tamanini, Luca Metric Geometry Functional Analysis Optimization and Control Probability 49Q22, 28A33 We show that the Hellinger-Kantorovich distance can be expressed as the metric infimal convolution of the Hellinger and the Wasserstein distances, as conjectured by Liero, Mielke, and Savaré. To prove it, we study with the tools of Unbalanced Optimal Transport the so called Marginal Entropy-Transport problem that arises as a single minimization step in the definition of infimal convolution. Careful estimates and results when the number of minimization steps diverges are also provided, both in the specific case of the Hellinger-Kantorovich setting and in the general one of abstract distances. |
| title | The infimal convolution structure of the Hellinger-Kantorovich distance |
| topic | Metric Geometry Functional Analysis Optimization and Control Probability 49Q22, 28A33 |
| url | https://arxiv.org/abs/2503.12939 |