Welcome to the archived materials for the graduate course An Introduction to Large Deviation Theory, which took place in Autumn 2025 at the University of Oulu.
This course explores the asymptotic behavior of remote tail probabilities for sums of random variables and stochastic processes. The notes below cover the transition from elementary combinatorial arguments to the general Gärtner-Ellis principle and its applications to finite-state Markov chains.
Lecture Notes
- Lecture 01 Introduction
- Lecture 02 Combinatorial arguments, method of Types
- Lecture 03 Cramér’s theorem in
- Lecture 04 Some backgrounds
- Lecture 05 General principles
- Lecture 06 LDP on topological vector spaces
- Lecture 07 Gärtner-Ellis theorem.
- Lecture 08 Case study: finite-state Markov chains