Oxford Lectures 2025
From Werner KRAUTH
My 2025 Public Lectures at the University of Oxford (UK), entitled Algorithms and computations in theoretical physics, run from 21 January 2025 through 11 March 2025.
Lecture 1: 21 January 2025
We start our parallel exploration of physics and of computing with the concept of sampling, the process of producing examples (“samples”) of a probability distribution. In week 1, we consider “direct” sampling (the examples are obtained directly) and, among the many connections to physics, will come across the Maxwell distribution. In 1859, it marked the beginning of the field of statistical physics.
Here are the notes for the first lecture (21 January 2025).
Lecture 2: 28 January 2025
We start with a Special Topic A, where we supplement the first Lecture with two all-important special topics that explore the meaning of convergence in statistics, and the fundamental usefulness of statistical reasoning. We can discuss them here, in the direct-sampling framework, but they are more generally relevant. The strong law of large numbers, for example, will turn into the famous ergodic theorem for Markov chains.
Here are the notes for Special Topic A (28 January 2025).
Then, in this second lecture proper, we consider Markov-chain sampling, from the adults' game on the Monte Carlo heliport to modern ideas on non-reversibility. We discuss a lot of theory, but also six ten-line pseudo-code algorithms, none of them approximate, and all of them as intricate as they are short.
