Universal concentration for sums under arbitrary dependence
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908864536903680 |
|---|---|
| author | Louart, Cosme Tan, Sicheng |
| author_facet | Louart, Cosme Tan, Sicheng |
| contents | We present a universal concentration bound for sums of random variables under arbitrary dependence, and we prove that it is asymptotically optimal for broad families of marginals admitting a uniform integrable tail-quantile envelope. The bound follows directly from the subadditivity of expected shortfall, a property well known in the risk-measure literature. Our sharpness result relies on an explicit construction of asymptotically extremal couplings. We furthermore provide practical sufficient conditions -- based on convex transformation order comparisons with exponential and power-law envelopes -- under which the bound admits simple, explicit tail profiles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03518 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Universal concentration for sums under arbitrary dependence Louart, Cosme Tan, Sicheng Probability Statistics Theory Primary 60E15, Secondary 60F10, 60E05 We present a universal concentration bound for sums of random variables under arbitrary dependence, and we prove that it is asymptotically optimal for broad families of marginals admitting a uniform integrable tail-quantile envelope. The bound follows directly from the subadditivity of expected shortfall, a property well known in the risk-measure literature. Our sharpness result relies on an explicit construction of asymptotically extremal couplings. We furthermore provide practical sufficient conditions -- based on convex transformation order comparisons with exponential and power-law envelopes -- under which the bound admits simple, explicit tail profiles. |
| title | Universal concentration for sums under arbitrary dependence |
| topic | Probability Statistics Theory Primary 60E15, Secondary 60F10, 60E05 |
| url | https://arxiv.org/abs/2601.03518 |