I would almost bet that the two functions are not the same, even in the limit as it becomes a Poisson distribution plus whatever the last rows do.

A Gaussian distribution, I think. But they're certaintly not the same function, and it should be immediately obvious to a math grad with experience in physics. The sinc function, for one, has secondary maxima (its plot in the article is very convenienty cropped to allow pretending those don't exist). Just put a hair in the path of a laser beam and you will see the local maxima in light intensity! Their "single-slit" string procedure, on the other hand, can only generate a single central peak. This really makes no sense at all.