Analysis Tools and Asymptotic Methods

摘要

So far we have dealt mostly with relatively simple situations, where the Hamiltonian is additive, and then the resulting B-G distribution is I.I.d. But this is seldom the case in reality. Most models in physics, including those that will prove relevant for information theory, as we shall see in the sequel, are much more complicated, more difficult, but also more interesting. More often than not, they are so complicated and difficult, that they do not lend themselves to closed-form analysis at all. In some cases, analysis is still possible, but it requires some more powerful mathematical tools and techniques, which suggest at least some asymptotic approximations. The purpose of this section is to prepare these tools, before we can go on to the more challenging settings.