Concentration for random Euclidean combinatorial optimization
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866912942505590784 |
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| author | D'Achille, Matteo Mattesini, Francesco Trevisan, Dario |
| author_facet | D'Achille, Matteo Mattesini, Francesco Trevisan, Dario |
| contents | We prove concentration bounds for random Euclidean combinatorial optimization problems with $p$--costs. For bipartite matching and for the (mono- and bi-partite) traveling salesperson problem in dimension $d\ge 3$, we obtain concentration at the natural energy scale $n^{1-p/d}$ for $1\le p<d^2/2$. Our method combines a Poincaré inequality with a robust geometric mechanism providing uniform bounds on the edges of optimizers. We also formulate a conjectural $p\!\to\!q$ transfer principle for the $p$--optimal matching which, if true, would extend the concentration range to all $p\ge 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21851 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Concentration for random Euclidean combinatorial optimization D'Achille, Matteo Mattesini, Francesco Trevisan, Dario Probability Optimization and Control We prove concentration bounds for random Euclidean combinatorial optimization problems with $p$--costs. For bipartite matching and for the (mono- and bi-partite) traveling salesperson problem in dimension $d\ge 3$, we obtain concentration at the natural energy scale $n^{1-p/d}$ for $1\le p<d^2/2$. Our method combines a Poincaré inequality with a robust geometric mechanism providing uniform bounds on the edges of optimizers. We also formulate a conjectural $p\!\to\!q$ transfer principle for the $p$--optimal matching which, if true, would extend the concentration range to all $p\ge 1$. |
| title | Concentration for random Euclidean combinatorial optimization |
| topic | Probability Optimization and Control |
| url | https://arxiv.org/abs/2602.21851 |