Year: 2026
Type: preprint
Abstract: We prove that for every finite connected simple graph $G$ on $n$ vertices with minimum degree $k\geq 2$, there is a coupling of its uniform spanning tree and its random $1$-out subgraph under which the expected number of differing edges is $O(n\log (k)/\sqrt{k})$. More generally, we establish analogous couplings between a wide class of determinantal processes and their corresponding $1$-out processes, including Kalai's determinantal hypertrees, with expected symmetric difference negligible compared to the size of the determinantal set. While the graphical case admits a surprisingly short and elegant proof, the more general result requires establishing an asymptotic equipartition property for the determinantal measures in this class, from which we also derive exponential growth rates for the homology torsion of determinantal hyperforests in higher-dimensional regular high-degree complexes.
Source: arXiv (Cornell University)
Authors: Mészáros, András, Peled, Yuval
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Israel Science Foundation
OpenAlex ID: W7221097833