Subinvariant kernel dynamics

James Tian

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arXiv · 2602.01432

Subinvariant kernel dynamics

James Tian

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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.

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James Tian. 2026-02-01. Subinvariant kernel dynamics. https://arxiv.org/abs/2602.01432

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