Hardcore Model undirected graph G(V,E)of max-degree A fugacity parameter >0 each independent set in G is assigned a weight: w(I)=λII distribution u over all independent sets in G: w(I) (I)=Eru(① =1:uniform distribution over independent setsHardcore Model • fugacity parameter λ>0 • each independent set I in G is assigned a weight: • distribution μ over all independent sets in G: undirected graph G(V, E) of max-degree Δ w(I) = ￾|I| µ(I) = w(I) P I w(I) • λ=1: uniform distribution over independent sets