Brownian motion and Markov processes, sequence of ingredients

• We want to study a physical system which evolves towards equilibrium, from given initial conditions.
• Markov chains are intimately linked with the physical process of diffusion.
• From a Markov chain we can then derive the conditions for detailed balance and ergodicity. These are the conditions needed for obtaining a steady state.
• The widely used algorithm for doing this is the so-called Metropolis algorithm, in its refined form the Metropolis-Hastings algorithm.

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