Non-asymptotic survival thresholds for finite-size habitats

Develop non-asymptotic bounds and characterizations for the principal Dirichlet eigenvalue and the resulting survival thresholds in finite-size random graph habitats with sink vertices, going beyond the asymptotic (large-network) regime analyzed in the paper.

Background

The main results provide asymptotic laws and sharp thresholds for the principal Dirichlet eigenvalue in large Erdős–Rényi habitats, leading to high-probability survival criteria as network size grows.

The authors explicitly state that understanding non-asymptotic regimes relevant for finite-size habitats remains open, indicating the need for finite-n spectral and probabilistic bounds that translate into survival guarantees without taking limits.