TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysLectNotes.100
TI  - Numerical aspects of large deviations
PY  - 2025/09/30
UR  - https://www.scipost.org/SciPostPhysLectNotes.100
JF  - SciPost Physics Lecture Notes
JA  - SciPost Phys. Lect. Notes
SP  - 100
A1  - Hartmann, Alexander K.
AB  - An introduction to numerical large-deviation sampling is provided. First, direct biasing with a known distribution is explained. As simple example, the Bernoulli process 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.
ER  -

@Article{10.21468/SciPostPhysLectNotes.100,
	title={{Numerical aspects of large deviations}},
	author={Alexander K. Hartmann},
	journal={SciPost Phys. Lect. Notes},
	pages={100},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhysLectNotes.100},
	url={https://scipost.org/10.21468/SciPostPhysLectNotes.100},
}