R. Banuelos - Lecture Materials

Title: "Finite Dimensional Distributions. What can you do with them?"

Slides

Abstract: In these talks we will explain how a number of problems, including some well known, unsolved, conjectures on the study of eigenvalues and eigenfunctions of Brownian motion and other Levy processes, can be reduce to the study of the finite dimensional distributions of the process. We will focus on the ideas rather than the technicalities.

Prerequisites: Basic properties of the heat semigroup of Brownian motion and other Levy processes, such as the rotationally invariant stable processes, will essentially be enough. Some of the material from Richard Bass course will be useful including his "reference 3" on stochastic calculus for jump processes

Some references:

A few pages from the following books:

  1. R. Bass: "Probabilistic Techniques in Analysis," Chapter II, especially section 4, pages 221-234.
  2. M. Loss and E. Lieb, "Analysis, Second Edition," Chapter 3.
Also useful will be to have a look at the introductions several of my papers. I put these together as a single pdf file title "introductions.pdf" and for the more ambitious ones, they can also read "gaps.pdf".