The Monte Carlo Method

The Monte-Carlo Method

The Monte Carlo Method

The Monte Carlo method is often referred to as a ‘computer experiment’. One might think of this as a way of conveying the fact that the output of simulations is not an equation, as in conventional theory. Instead, numbers appear on the computer screen in somewhat the same way that numbers appear on a measuring device in the laboratory. Thus there is the implication that somehow simulations are ...

The Monte Carlo Method

The Monte Carlo method is often referred to as a ‘computer experiment’. One might think of this as a way of conveying the fact that the output of simulations is not an equation, as in conventional theory. Instead, numbers appear on the computer screen in somewhat the same way that numbers appear on a measuring device in the laboratory. Thus there is the implication that somehow simulations are ...

Graphs & The Monte Carlo Method

Definition 4. BBP is the class of languages L that have a poly time algorithm A that for any string x, and a long random string r, • x ∈ L⇒ Pr[A(x, r)rejects] ≤ 1/100 • x 6∈ L⇒ Pr[A(x, r)accepts] ≤ 1/100 Observation 5. By repeating this algorithm k times with random strings r1...rk, the probability that the majority of the outcomes is incorrect is 1/2Ω(k) (proved this with Chernoff bound on a p...

The quantum Monte Carlo method

Quantum Monte Carlo is an important and complementary alternative to density functional theory when performing computational electronic structure calculations in which high accuracy is required. The method has many attractive features for probing the electronic structure of real atoms, molecules and solids. In particular, it is a genuine many-body theory with a natural and explicit description ...