Generalised convexity with respect to families of affine maps
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910587374534656 |
|---|---|
| author | Kabluchko, Zakhar Marynych, Alexander Molchanov, Ilya |
| author_facet | Kabluchko, Zakhar Marynych, Alexander Molchanov, Ilya |
| contents | The standard convex closed hull of a set is defined as the intersection of all images, under the action of a group of rigid motions, of a half-space containing the given set. In this paper we propose a generalisation of this classical notion, that we call a $(K,\mathbb{H})$-hull, and which is obtained from the above construction by replacing a half-space with some other convex closed subset $K$ of the Euclidean space, and a group of rigid motions by a subset $\mathbb{H}$ of the group of invertible affine transformations. The main focus is put on the analysis of $(K,\mathbb{H})$-convex hulls of random samples from $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_07887 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Generalised convexity with respect to families of affine maps Kabluchko, Zakhar Marynych, Alexander Molchanov, Ilya Metric Geometry Probability Primary: 60D05, secondary: 52A01, 52A22 The standard convex closed hull of a set is defined as the intersection of all images, under the action of a group of rigid motions, of a half-space containing the given set. In this paper we propose a generalisation of this classical notion, that we call a $(K,\mathbb{H})$-hull, and which is obtained from the above construction by replacing a half-space with some other convex closed subset $K$ of the Euclidean space, and a group of rigid motions by a subset $\mathbb{H}$ of the group of invertible affine transformations. The main focus is put on the analysis of $(K,\mathbb{H})$-convex hulls of random samples from $K$. |
| title | Generalised convexity with respect to families of affine maps |
| topic | Metric Geometry Probability Primary: 60D05, secondary: 52A01, 52A22 |
| url | https://arxiv.org/abs/2202.07887 |