Outline for the kick-off and theory period

1. Motivation
   The phenomenology of queues in buffers; asymptotics of queue-length distributions; the Hurst phenomenon; long-range dependence and level shifts.

2. The Elements of Large Deviation Theory
   Prehistory - Boltzmann and Einstein; history - Cramér and risk theory; some useful tricks with Exponential Asymptotics; the intuition to be gained from a simple coin-tossing experiment; when we can expect random variables to display Large Deviation behaviour and how to calculate the rate-function when they do.

3. The Main Principles of Large Deviation Theory I
   The main principles stated without proof, but with heuristic explanations: Exponential Asymptotics for Good Sets; Concentration of Probability; Varadhan's Theorem - the Asymptotics of Integrals; The Contraction Principle.

4. Some Simple Applications
   Statistical multiplexing - increased utilisation at the expense of a calculated risk; Shannon's Theorem - an illustration from information theory.

5. The Main Principles of Large Deviation Theory II
   The main principles proved for probability distributions on Euclidean space; the existence of a rate-function in the case of weak-dependence.