Whoops, I thought I was answering a question about my rejection sampling article. My mistake. I'll address this though. 1) No it doesn't. I don't make any dist

Whoops, I thought I was answering a question about my rejection sampling article. My mistake. I'll address this though. 1) No it doesn't. I don't make any distributional claims for these calculations. You're right. I haven't addressed questions like P(>90%|t=1000). 2) Actually no, it doesn't take the variance to 0. For any given t, the Markov approximation is equal to the expected value of the given atom at time t. There is a variance for every atom count at every time point. I didn't address calculating variance at all. We're speaking in expected values here, the interpretation of 54.8 atoms at time t is the same as the average american household having 2.5 children. Something I addressed in a comment when I posted this on reddit was that the Markov chain approach is the theoretical mean. If you were to actually observe a decay process like this in the real world, it would essentially be one possible realization of the simulated example. As far as the Pareto distribution is concerned, I didn't know that actually. That's really interesting.