On the approximation of permutons
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915976988065792 |
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| author | Maga, Balázs |
| author_facet | Maga, Balázs |
| contents | We study the optimal rectangular-discrepancy approximation of permutons by finite permutations. We transfer bounds from discrepancy theory to this more restricted setup. Moreover, we show that superlinear approximation can occur only for permutons supported by graphs of measure-preserving functions, and demonstrate how the local regularity of this function obstructs approximability. We also consider the biased Brownian separable permuton and prove a lower bound on its approximation error by showing that its supporting measure-preserving function has Lipschitz points almost surely. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02298 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the approximation of permutons Maga, Balázs Combinatorics Probability Primary 05A05, Secondary 05C80, 11K38, 60C05 We study the optimal rectangular-discrepancy approximation of permutons by finite permutations. We transfer bounds from discrepancy theory to this more restricted setup. Moreover, we show that superlinear approximation can occur only for permutons supported by graphs of measure-preserving functions, and demonstrate how the local regularity of this function obstructs approximability. We also consider the biased Brownian separable permuton and prove a lower bound on its approximation error by showing that its supporting measure-preserving function has Lipschitz points almost surely. |
| title | On the approximation of permutons |
| topic | Combinatorics Probability Primary 05A05, Secondary 05C80, 11K38, 60C05 |
| url | https://arxiv.org/abs/2605.02298 |