A 2^N\times M - node spider network is a set of M-layers each of which has 2^N nodes which can be represented by N-bit binary numbers. A site in layer r may be represented by an N-bit integer. The site in the r^{th} layer ...

In this thesis, we study simple stochastic models that show rich and interesting behavior. The plan of the thesis is as follows: after a brief introduction and overview of the work in Chapter 1, Chapter 2 begins with a ...

This thesis defines a variation of a regular random graph called the Random Locally Tree-like Layered Lattice (RLTL). Such lattices are of interest because the Bethe approximation becomes asymptotically exact on them. ...

In this thesis, we estimate the average ground state energy of spin glass models. Despite decades of study, there have been no exact explicit calculations for a mean field model of spin glass with finite ranged interactions. ...