Subinvariant kernel dynamics
Probability
2026-02-03 v1 Functional Analysis
Abstract
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.
Cite
@article{arxiv.2602.01432,
title = {Subinvariant kernel dynamics},
author = {James Tian},
journal= {arXiv preprint arXiv:2602.01432},
year = {2026}
}