Monte Carlo
Probability, detailed balance, and useful sampling.
Learning sequence
- Why the canonical distribution appears — Derive Boltzmann weights from a heat bath and form an estimator.
- Detailed balance and Metropolis–Hastings — Prove the acceptance ratio, including asymmetric proposals.
- Ising sampling and honest error bars — Derive spin-flip energy and the variance of correlated averages.
Read in sequence. Each lesson states its assumptions, derivation steps, and domain of validity.
