As a physicist, the moment when everything just clicked was when I realised that connected Feynman diagrams were basically the cumulants of that distribution.
Then almost everything in physics is about "what is the characteristic/moment/cumulant generating function?" and associated Legendre transforms
A little known bit of history is Feynman developed a diagrammatic method for expressing the moments of PGFs in his study of the stochastic theory of fission chains. This was before his work on QED. See:
Wow. I am not a physicist, but I use pdfs and moments and cumulants all the time. I came up with my own method to calculate cumulants for affine processes using some recursions, and they work. But if I hear you right, I might have stumbled upon something that Feynman did 70 years ago, and he probably did it better. Any good links you can recommend?
> As a physicist, the moment when everything just clicked was when I realised that connected Feynman diagrams were basically the cumulants of that distribution.
And the generating function of the cumulants is the logarithm of the generating function of the distribution (Fourier transform).
