Mike Liu

collaborators

4 papers

math.PR2026

Uniqueness and locality of the ground state of the disordered Monomer-Dimer models on independently weighted Unimodular BienaymÃ©-Galton-Watson trees

Mihyun Kang, Mike Liu

Consider a finite graph $G = (V (G), E (G))$ and two continuous weight distributions $I ¨ $ and $I^¾$ , for which we only assume that $I^¾$ is lower bounded. Next, independently draw weights…

math.PR2026

Optimal matching under size priority

NathanaÃ«l Enriquez, Mike Liu, Laurent MÃ©nard +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…

math.PR2025

Percolative properties of the random coprime colouring

Given $u$ and $v$ in $Z^{d}$ , say that $u$ is visible from $v$ if the segment from $u$ to $v$ contains exactly two elements, which are $u$ and $v$ . Take $X$ "uniformly at ra…

math.PR2025

Optimal Unimodular Matching

We consider sequences of finite weighted random graphs that converge locally to unimodular i.i.d. weighted random trees. When the weights are atomless, we prove that the matchings…