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Numerical Aspects of Large Deviations
by Alexander K. Hartmann
Submission summary
| Authors (as registered SciPost users): | Alexander K. Hartmann |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2412.04338v2 (pdf) |
| Code repository: | http://doi.org/10.57782/HXEGVF |
| Date accepted: | July 29, 2025 |
| Date submitted: | June 6, 2025, 8:27 a.m. |
| Submitted by: | Alexander K. Hartmann |
| Submitted to: | SciPost Physics Lecture Notes |
| for consideration in Collection: |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Computational |
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 $U(0,1)$ 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.
Author comments upon resubmission
thank you for the detailed report of the referees. I am pleased that
they are very positive. I have considered all recommendations
for the next version of the manuscript. Below you find detailed answers
to all recommendations.
Thus, the manuscript should now suitable for acceptance.
Yours faithfully
Alexander Hartmann
List of changes
Published as SciPost Phys. Lect. Notes 100 (2025)