AbstractWe study the Ising model on Z^3 with an externel field {\epsilon h_v} where h_v~N(0,1). We want to show that for any T lower than the critical temperature T_c, the long range order exsits as long as \epsilon is sufficiently small depending on T. This work extends previous results of Imbrie (1985) and Bricmont–Kupiainen (1988) from the very low temperature regime to the entire low tempe...
DescriptionModel selection and its diagnosis are foundational elements in modern statistical and machine learning applications that serve the purpose of obtaining reliable information and reproducible results. In this short course, we introduce the principles and theories on model selection and model averaging and their applications in high-dimensional regression. Model selection methods includ...