Some remarks on the Gram-Schmidt walk algorithm and consequences for Komlos conjecture
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910400096763904 |
|---|---|
| author | Bednorz, Witold Godlewski, Piotr |
| author_facet | Bednorz, Witold Godlewski, Piotr |
| contents | In this paper we improve the best known constant for the discrepancy formulated in the Komlos Conjecture. The result is based on the improvement of the subgaussian bound for the random vector constructed in the Gram-Schmidt Random Walk algorithm. Moreover, we present detailed argument for the smoothed analysis of this random vector. The analysis concerns a modification of a given matrix in the conjecture by a Gaussian type perturbation. Our result improves the recent paper in this direction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03534 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some remarks on the Gram-Schmidt walk algorithm and consequences for Komlos conjecture Bednorz, Witold Godlewski, Piotr Probability 60G15, 60G17 In this paper we improve the best known constant for the discrepancy formulated in the Komlos Conjecture. The result is based on the improvement of the subgaussian bound for the random vector constructed in the Gram-Schmidt Random Walk algorithm. Moreover, we present detailed argument for the smoothed analysis of this random vector. The analysis concerns a modification of a given matrix in the conjecture by a Gaussian type perturbation. Our result improves the recent paper in this direction. |
| title | Some remarks on the Gram-Schmidt walk algorithm and consequences for Komlos conjecture |
| topic | Probability 60G15, 60G17 |
| url | https://arxiv.org/abs/2404.03534 |