Stochastic Signatures of Phase Space Decomposition

Figure 1

A 𝑑=2 dimensional lattice of 𝑁=100 sites. One possible representation of such a lattice would be a 10×10 system. But, another representation that comprises 𝑁=100 sites would be the disjoint pair of lattices, a 6×6 lattice with 𝑁=36 sites and an 8×8 lattice with 𝑁=64 sites, linked at a common corner site (articulation point).