Abstract
The Monte–Carlo method is introduced as a generic tool for the solution of mathematical physics models by means of computer simulation. These problems range from simple one-dimensional integration to sophisticated multi-dimensional models involving elaborate geometries and complex system states. A historical introduction and an exposition of the basic idea are followed by a basic treatment of numerical integration and discussing methods of variance reduction like importance sampling and use of quasi-random sequences. Markov-chain Monte Carlo is presented as a powerful method to generate random numbers according to arbitrary, even extremely complicated distributions. A specific implementation in the form of the Metropolis–Hastings algorithm is offered.
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Širca, S. (2016). The Monte–Carlo Method. In: Probability for Physicists. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-31611-6_13
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DOI: https://doi.org/10.1007/978-3-319-31611-6_13
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