For random spanning trees with weights exp(-β ω_e) on K_n, edge overlap transitions from ~β to ~n as β grows past n, with local limit matching uniform ST for β = o(n/log n) and min ST for β > n log^λ n.
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Local limits of random spanning trees in random environment
For random spanning trees with weights exp(-β ω_e) on K_n, edge overlap transitions from ~β to ~n as β grows past n, with local limit matching uniform ST for β = o(n/log n) and min ST for β > n log^λ n.