Numerical Aspects of Large Deviations
arXiv:2412.04338 · doi:10.21468/SciPostPhysLectNotes.100
Abstract
An introduction to numerical large-deviation sampling is provided. First, direct biasing with a known distribution is explained. As simple example, the Bernoulli experiment is used throughout the text. Next, Markov chain Monte Carlo (MCMC) simulations are introduced. In particular, the Metropolis-Hastings algorithm is explained. As first implementation of MCMC, sampling of the plain Bernoulli model is shown. Next, an exponential bias is used for the same model, which allows one to obtain the tails of the distribution of a measurable quantity. This approach is generalized to MCMC simulations, where the states are vectors of random entries. This allows one to use the exponential or any other bias to access the large-deviation properties of rather arbitrary random processes. Finally, some recent research applications to study more complex models are discussed.
Lectures notes for lectures given at 2024 Les Houches Summer School on "Large deviations and applications". For C Codes see DARE (Oldenburg University research data repository) at doi.org/10.57782/HXEGVF. Revised version V02 contains now detailed overview over paper, section on needed numerical resources and overview over other approaches, plus small changes
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