Random projections beyond zero overlap
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917158358876160 |
|---|---|
| author | Wee, Timothy L. H. Tatikonda, Sekhar |
| author_facet | Wee, Timothy L. H. Tatikonda, Sekhar |
| contents | A random vector whose norm and overlap (inner product with an independent copy) concentrates is shown to have random low-dimensional projections that are approximately random Gaussians. Conversely, asymptotically random Gaussian projections imply these hypotheses. This extends and unites several existing results in geometric functional analysis and spin glasses. Applications include a large-system characterization of the joint law of cavity fields in the Sherrington-Kirkpatrick model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01248 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Random projections beyond zero overlap Wee, Timothy L. H. Tatikonda, Sekhar Probability 60K35, 60F05, 82B44 A random vector whose norm and overlap (inner product with an independent copy) concentrates is shown to have random low-dimensional projections that are approximately random Gaussians. Conversely, asymptotically random Gaussian projections imply these hypotheses. This extends and unites several existing results in geometric functional analysis and spin glasses. Applications include a large-system characterization of the joint law of cavity fields in the Sherrington-Kirkpatrick model. |
| title | Random projections beyond zero overlap |
| topic | Probability 60K35, 60F05, 82B44 |
| url | https://arxiv.org/abs/2312.01248 |