Monte Carlo Method
A class of computational algorithms that rely on repeated random sampling to obtain numerical solutions for complex physical systems.
Governing formula
I ≈ (1 / N) ∑_(i=1)^(N) f(X_i) (Central Limit Theorem)
SI unit
Stochastic Numerical Method
In depth
Monte Carlo methods evaluate multi-dimensional integrals and complex statistical mechanics systems where analytical solutions are impossible. Error decreases as 1/√N regardless of problem dimensionality.
Examples in the real world
Simulating neutron transport through nuclear reactor shielding and evaluating path integrals in quantum chromodynamics.