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math.PR2026
Uniqueness and locality of the ground state of the disordered Monomer-Dimer models on independently weighted Unimodular Bienaymé-Galton-Watson trees
Mihyun Kang, Mike Liu
Consider a finite graph and two continuous weight distributions and , for which we only assume that is lower bounded. Next, independently draw weights $(…
math.PR2026
Optimal matching under size priority
Nathanaël Enriquez, Mike Liu, Laurent Ménard +1
Past studies on the local limit of maximal weight matchings in edge-weighted large random graphs rely fundamentally on the assumption that the weights are atomless, which ensures t…