Monte Carlo simulation in statistical physics

By M. Wallin. 2005

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Polymers with spatial or topological constraints: Theoretical and computational results (2011, background): “Because at each Monte Carlo step, the probability of accepting the trial configuration depends only on the configuration at the previous step (and not on “older” ones), the MC evolution realizes a Markov chain [90, 92, 93] Starting from an initial conformation, the repeated application of the accept”
Geometric ergodicity of the Bouncy Particle Sampler (2018, background): “Markov chain Monte Carlo methods is a core requirement in many applications, e.g. in computational statistics [20], machine learning [1], molecular dynamics [6].”
Why Are Polar Surfaces of ZnO Stable (2017, unknown): “To address the challenge of the diverse structural and chemical conditions, we have applied Monte Carlo methods ( e.g. , refs 48 and 49) developed in statistical mechanics, and widely used in materials simulations ( e.g. , refs 50 − 52).”