Feynman diagrams without any physics
The article discusses the application of Feynman diagrams in solving problems related to Gaussian random variables. It explains how Isserlis' theorem can be utilized to calculate the expectation values of products of these variables. The author illustrates the process using combinatorial methods and visual representations to simplify complex calculations.
- ▪Feynman diagrams can be applied to elementary probability theory, particularly with Gaussian random variables.
- ▪Isserlis' theorem provides a method for calculating the mean of products of Gaussian variables through perfect matchings.
- ▪The article demonstrates how to visualize and simplify calculations using Feynman diagrams.
Opening excerpt (first ~120 words) tap to expand
A tale from elementary probability theoryFeynman diagrams are associated with complicated physics, but they can also be found hiding in relatively simple questions about Gaussian random variables.For example, suppose I asked you to calculate the expectation valuewhere each is a (not necessarily independent) normal random variable with zero mean. Say I want the answer in terms of the covariances between the variables.If you are especially visually-minded (and considerably brilliant) you may find yourself eventually drawing the following diagrams……on your way to producing the answer, which is in this case isHere’s some Julia code approximately showing that this formula is correct.julia> using Distributions, Statisticsjulia> Σ = let A = rand(4,4); A'A end # make a symmetric matrix4×4…
Excerpt limited to ~120 words for fair-use compliance. The full article is at Github.
