Basic properties of the infinite critical-FK random map (Q2412680)

The paper studies the critical Fortuin-Kasteleyn (cFK) random map model of size \(n\) (\(=\) of \(n\) edges) and of parameter \(q\). The model is defined by the probability law \(Q_n^{(q)}\) on the set of all subgraph-rooted maps on \(n\) edges. The probability \(Q_n^{(q)}\) is proportional to the partition function of the Potts model. The main result of the paper states that for each \(q\in [0,\infty)\), \(Q_n^{(q)}\rightarrow Q_\infty^{(q)}\) in distribution.