Year: 2025
Type: preprint
Abstract: Let $H_n$ be the row space of a signed adjacency matrix of a $C_4$-free bipartite bi-regular graph in which one part has degree $d(n)\to\infty$ and the other part has degree $k+1$ where $k\geq 1$ is a fixed integer. We show that the local limit as $n\to \infty$ of the determinantal process corresponding to the orthogonal projection on $H_n$ is a variant of a Poisson$(k)$ branching process conditioned to survive. This setup covers a wide class of determinantal processes such as uniform spanning trees, Kalai's determinantal hypertrees, hyperforests in regular polytopal complexes, discrete Grassmanians and incidence matroids, as long as their degree tends to $\infty$.
Source: arXiv (Cornell University)
Authors: Nachmias, Asaf, Peled, Yuval
Institutions: Tel Aviv University, Hebrew University of Jerusalem
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416247185
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