Renormalization methods with applications to spin systems and finance.

摘要

In this thesis, I propose three different numerical techniques for computing a renormalized Hamiltonian, or equivalently, the density of the distribution of renormalized variables. I apply these techniques to the two-dimensional Ising model, the Discrete Gaussian model and to the analysis of the US Treasury yield curve. Futhermore, I consider the Gaussian factor portfolio model of finance; using the expression for renormalized density, I suggest several fast algorithms for computing quantities of practical importance in portfolio management.