The rival coffee shop problem
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913237811855360 |
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| author | Casado, Javier Cuerno, Manuel |
| author_facet | Casado, Javier Cuerno, Manuel |
| contents | We show some estimations for the Coffee Shop Problem with a modification respect the original statement: there is a rival competing against us. We present different results based on how fast the rival is able to grow. As main tool, we use a variation of the Wasserstein distance (the Signed Wasserstein Distance presented by Piccoli, Rossi and Tournus in "A Wasserstein norm for signed measures, with application to non local transport equation with source term"), that allow us to work with finite signed measures and fits our problem. We are able to obtain similar inequalities with this distance to the ones produced by the canonical Wasserstein distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_04535 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The rival coffee shop problem Casado, Javier Cuerno, Manuel Metric Geometry Classical Analysis and ODEs 49Q20, 28A33, 30L15, 49Q22 We show some estimations for the Coffee Shop Problem with a modification respect the original statement: there is a rival competing against us. We present different results based on how fast the rival is able to grow. As main tool, we use a variation of the Wasserstein distance (the Signed Wasserstein Distance presented by Piccoli, Rossi and Tournus in "A Wasserstein norm for signed measures, with application to non local transport equation with source term"), that allow us to work with finite signed measures and fits our problem. We are able to obtain similar inequalities with this distance to the ones produced by the canonical Wasserstein distance. |
| title | The rival coffee shop problem |
| topic | Metric Geometry Classical Analysis and ODEs 49Q20, 28A33, 30L15, 49Q22 |
| url | https://arxiv.org/abs/2304.04535 |