Robin PEMANTLE Cornell 2009 Summer School Page

Version of 17 July 2009

There will be five lectures on generating functions and one on probabilistic number theory. The lectures on generating functions will be accompanied by lecture notes. These will be revised during or shortly after the two-week summer school, but for now I am posting a preliminary version, no doubt riddled with errors, in order to accomodate those anyone wanting access ahead of time. You can tell they have been revised when the Version date is no longer June.

These are lecture notes, not lecture slides. There will be no lecture slides. The lectures themselves, except for Lecture 4 which is largely pictorial, will be chalk talks, presenting the main ideas and avoiding lengthy derivations. The main purpose of the notes is to give some of the details omitted in the talks, allowing the audience to go over these later, or to browse them in real time during the lecture. I say "some of the details" because many aspects of the background appear in the lecture notes in a form condensed from other sources. I have tried to give precise citations to sources where a full treatment is given.

Links are given below to the lecture notes, as well as to readings that provide more detailed background for each lecture.

Lecture 0: this is unrelated to the other five. It is on probabilistic number theory. There are no lecture notes for this talk, but it is based on this preprint.

Square subproducts

Table of contents and references for the remaining five lectures

Lecture 1: Fourier-Laplace integrals in probability, combinatorics and statistics

Multivariate Fourier-Laplace integrals

Volume estimation via Newton diagram

Statistical example

Lecture 2: Generating functions in probability and combinatorics

Introduction to generating functions

Transfer theorems

Lecture 3: The smooth case: Gaussian behavior

Survey paper on examples in the smooth case

Lecture 4: Quantum random walks

1-D quantum random walks

2-D quantum random walks

Lecture 5: Proofs for smooth points

Overview paper

Paper on quadratic points

Some more links of possible interest

Asymptotics of multivariate sequences research page

Homepage for Robin Pemantle's 2007 REU on quantum random walks

To Robin's homepage