Subinvariant kernel dynamics
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866912868112269312 |
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| author | Tian, James |
| author_facet | Tian, James |
| contents | We study positive definite kernels pulled back along a finite family of self-maps under a subinvariance inequality for the associated branching operator. Iteration produces an increasing kernel tower with defect kernels. Under diagonal boundedness, the tower has a smallest invariant majorant, with a canonical defect space realization and an explicit diagonal harmonic envelope governing finiteness versus blow-up. We also give probabilistic and boundary representations: a Gaussian martingale model whose quadratic variation is the defect sequence, and canonical Doob path measures with a boundary feature model for the normalized defects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01432 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Subinvariant kernel dynamics Tian, James Probability Functional Analysis Primary: 46E22, secondary: 31C20, 37C30, 47A20, 60G15 We study positive definite kernels pulled back along a finite family of self-maps under a subinvariance inequality for the associated branching operator. Iteration produces an increasing kernel tower with defect kernels. Under diagonal boundedness, the tower has a smallest invariant majorant, with a canonical defect space realization and an explicit diagonal harmonic envelope governing finiteness versus blow-up. We also give probabilistic and boundary representations: a Gaussian martingale model whose quadratic variation is the defect sequence, and canonical Doob path measures with a boundary feature model for the normalized defects. |
| title | Subinvariant kernel dynamics |
| topic | Probability Functional Analysis Primary: 46E22, secondary: 31C20, 37C30, 47A20, 60G15 |
| url | https://arxiv.org/abs/2602.01432 |