We study the problem of recovering a planted matching in randomly weighted complete
bipartite graphs K n, n. For some unknown perfect matching M∗, the weight of an edge is …

We establish the soundness of the replica symmetric ansatz introduced by M. Mézard and G.
Parisi for the minimum matching problem in the pseudo-dimension d mean field model for …

We study the bond percolation game and the site percolation game on the rooted Galton-
Watson tree $ T_ {\chi} $ with offspring distribution $\chi $. We obtain the probabilities of win …

We establish the soundness of the replica symmetric ansatz introduced by M. Mezard and G.
Parisi for minimum matching and the traveling salesman problem in the pseudo-dimension d …

Random graphs are mathematical models for understanding real-world networks. Important
properties can be captured, processes studied, and rigorous predictions made. Phase …