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A while ago I thought about the fact that if you repeatedly apply f(x)=2+x/2 to a number, you approach 4. What happens if you repeatedly apply, with a 50/50 cha
by jon_richards 9y ago
A while ago I thought about the fact that if you repeatedly apply f(x)=2+x/2 to a number, you approach 4. What happens if you repeatedly apply, with a 50/50 chance, either x/2 or x+2 to a distribution? What distribution do you get?
I could find a lot of analysis using matrices in discrete math, but I couldn't find much for continuous distributions. I haven't gotten all the way through reading this, but it seems like it could be helpful.
- JadeNB 9y agoThis sounds quite a bit like a probabilistic version of the Collatz problem (https://en.wikipedia.org/wiki/Collatz_conjecture https://en.wikipedia.org/wiki/Collatz_conjecture). I thought I'd seen results on this before, but a quick Google result doesn't turn anything up. (Instead, Google results want to discuss probabilistic heuristics for why the deterministic Collatz conjecture holds.)
- jon_richards 9y agoHmm. Thanks for the thought. I'm not sure how related it is, but I might find something in the attempted solutions. The original idea behind this was to figure out how to study the stability of certain probabilistic transformations. The hope was to be able to make transformations that are good at detecting non-random inputs, particularly in time-series data. Could potentially be used in a similar way to neural-nets.
- jon_richards 9y agoAfter reading through his notes, I think my question differs significantly from his. He focuses on the extreme ends of ramp functions, which remain a single size, despite the domain in between them growing. The resulting function is therefor a piecewise transformation (is that the right term?) of the original function, rather than the exact same function or a simple transformation of it.