My research project involves extending some of the limit theorems for the Curie-Weiss model, an n vertex graph that randomly assigns to each vertex the value + or – 1. Depending on specific parameter values, when we consider the sample mean of all spins (vertex) and find its limiting distribution (after correctly standardising) we obtain different distributions for different values of the parameters. In particular there is a parameter that exhibits critical phenomena where values either side of this critical value give vastly different distributions. My project will involve varying the parameter such that, instead of it being a constant value, is a sequence that converges to the critical value. By changing the speed of convergence and the sign of convergence, I want to explore the range of limiting distributions for the sample mean over all spins.
Aram Perez is enrolled in Monash University’s Bachelor of Science Advanced – Research (Honours) with mathematics as his extended major. He is passionate about mathematics and aims to continually expand the depth of his knowledge of concepts within all fields of mathematics and its applications in the natural sciences and computer science.