Monte Carlo and Quantum Monte Carlo

We will cover basics of Monte Carlo and selected quantum Monte Carlo methods for the simulations of quantum many-body systems on (classical) computers.
We cover discrete and continuos systems at the same time.

Syllabus:
Probability theory, law large numbers, central limit theorem
Markov Chains on graphs: proving convergence, mixing times
Langevin & Fokker-Planck equations
Variational principle & VMC: local energy, gradients, natural gradients, cusp conditions
Restricted Bolzmann Machine as VMC ansatz
DMC: naive & Importance sampling algorithms, sign-problem
PIMC for continuos and lattice systems: ring-polymer, loop algorithm, sign-problem
A bit of complexity theory