Denys Wilkinson Building, Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH
Professor , Ecole Normale Superieure Paris and Rudolf Peierls Centre for Theorectial Physics, Oxford University
Professor Werner Krauth
Times and dates: weeks 1-8 of HT 2026, Tue 2-4pm in the Fisher Room
These public lectures introduce to the vast field of algorithms and computing from the view- point of theoretical physics and its interface with statistics. It is also a practical, example- based, primer on subjects such as Markov chains, molecular dynamics, phase transitions, path integrals, superfluids and Bose-Einstein condensation, among others. The lectures stress the rigorous foundations and modern developments in mathematics (mixing, non-reversibility, perfect sampling,... ) and physics (entropic phase transition, Kosterlitz-Thouless physics, cold atoms,... ), yet is entirely based on miniature Python programs. It will prepare advanced undergraduates in physics/math for the requirements of modern-day research across many fields, with the huge role played by algorithmic thinking, its power, paradoxes and intricacies.
Contents:
Sampling, Markov chains
– Direct Sampling: From basic rejection sampling to Walker’s method of aliases.
– Reversible and non-reversible Markov chains: One-dimensional motion.
– Mixing and relaxation times, the cutoff phenomenon.
– Perfect sampling: Stopping rules, Coupling from the past.
– Data analysis: From the strong law of large numbers to the ergodic theorem for Markov chains.
Classical hard disks and hard spheres
– Molecular dynamics: From Alder and Wainwright (1957) to modern heap-based scheduling.
– Hard-sphere Monte Carlo: From Metropolis et al. (1953) to the event-chain Monte Carlo.
– Entropic phase transitions: melting.
– One-dimensional simple exclusion models.
Quantum Monte Carlo
– Density matrices and path integrals.
– Superfluidity and condensate fractions: a path-integral point of view.
– Sampling of path integrals: the L ́evy construction (Gaussian bridge).
– Ideal bosons from a path-integral perspective.
– Path integrals and random manifolds. Roughness exponents, fractional Brownian motion.
Spin systems: samples and exact solutions
– Ising Markov chains: from Glauber dynamics to modern cluster algorithms.
– Mixing and relaxation times: modern mathematics and cutting-edge algorithms.
– 2D XY model and the harmonic model: Reversible and non-reversible Markov-chain algorithms. Kosterlitz- Thouless physics.
– Perfect sampling: semi-order
– Modern sampling algorithms derived from the Onsager solution.
From Monte Carlo sampling to Machine learning – Inference and Bayesian statistics
– Learning and classification
Literature:
- W. Krauth, ”Statistical Mechanics, Algorithms and Computations” (Oxford University Press, 2006; Second edition: 2024)
- D. A. Levin and Y. Peres, ”Markov Chains and Mixing Times (Second Edition)” (AMS, 2017)
- L. Wasserman, ”All of Statistics, A Concise Course in Statistical Inference” (Springer, 2005)