Network theory | Stochastic models | Graph theory | Applied mathematics
Weighted planar stochastic lattice
Physicists often use various lattices to apply their favorite models in them. For instance, the most favorite lattice is perhaps the square lattice. There are 14 Bravais space lattice where every cell has exactly the same number of nearest, next nearest, nearest of next nearest etc. neighbors and hence they are called regular lattice. Often physicists and mathematicians study phenomena which require disordered lattice where each cell do not have exactly the same number of neighbors rather the number of neighbors can vary wildly. For instance, if one wants to study the spread of disease, viruses, rumors etc. then the last thing one would look for is the square lattice. In such cases a disordered lattice is necessary. One way of constructing a disordered lattice is by doing the following. Starting with a square, say of unit area, and dividing randomly at each step only one block, afterpicking it preferentially with respect to ares, into four smaller blocks creates weighted planar stochastic lattice (WPSL). Essentially it is a disordered planar lattice as its block size and their coordination number are random. (Wikipedia).
