Timeline for Why does random noise in recurring task periods result in uniform period offsets?

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Aug 17, 2021 at 16:06	comment	added	D.W.♦		@JonasKölker, I don't know of a formal proof that "Gaussian mod m is approximately uniform when m is small compared to the standard deviation of the Gaussian". Perhaps you could ask for that on Math.SE?
Aug 17, 2021 at 7:29	comment	added	Jonas Kölker		Here's my first idea: if you have a derived continuous distribution $Y_n$ with finite mean and variance that's an increasing function of $n$, maybe with more constraints, by choosing $n$ large enough the $\textrm{mod}$ buckets become arbitrarily fine grained relative to $Y_n$. Since $Y_n$ is continuous the differences across neighboring buckets can be made arbitrarily small by making the buckets smaller (and the convergence gap to Z can be made arbitrarily small), therefore we can get arbitrarily close to a uniform. Does this work, if formalized? Do I need uniform continuity?
Aug 17, 2021 at 7:19	comment	added	Jonas Kölker		I had noticed that if $D = \{k, k+1\}$ you see binomial distributions the first few ($n$?) iterations. The CLT had come to mind, but I didn't know how to get from converging-to-Gaussian to converging-to-uniform, exactly the step where you appeal to intuition. Do you know of a rigorous proof of that step?
Aug 17, 2021 at 2:56	history	answered	D.W.♦	CC BY-SA 4.0