Timeline for Size doubling amoeba

Current License: CC BY-SA 4.0

14 events

when toggle format	what		by	license	comment
yesterday	vote	accept	Nate River
yesterday	answer	added	ofer zeitouni		timeline score: 4
2 days ago	comment	added	user65023		If $\epsilon > 2(\frac{1}{2})^{({1}/{p})}$, then $\lim_{t\in \infty} S_t^{\mbox{max}}=\infty$ almost surely. This follows from the strong law of large numbers. If you track the size of the original amoeba and pick one copy when it splits, then the expected size is $(\epsilon^p 2^q)^{n} \to \infty$, if $\epsilon^p 2^q >1$. By the strong law (or ergodic theorem), the size of this amoeba goes to infinity almost surely. This doesn't take into account that there might be on the order of $2^{pn}$ amoebas at stage $n$, so there is likely a better bound. Probably stating the obvious here.
Dec 15 at 6:55	comment	added	Nate River		@mathworker21 It is the size before splitting. And yes, each amoeba evolves according to the same rule.
Dec 15 at 0:27	comment	added	mathworker21		Also, you said "it" after talking about the species, which I think you didn't mean to do. Is each amoeba evolving according to the rule (simultaneously)?
Dec 15 at 0:26	comment	added	mathworker21		Does $S$ denote the starting size of the amoeba (which you said is $1$) or the size right before splitting?
Dec 14 at 14:24	history	edited	Nate River	CC BY-SA 4.0	deleted 90 characters in body
Dec 14 at 13:56	comment	added	user531372		Great question. +1
Dec 14 at 12:38	comment	added	Nate River		@M.G. Unfortunately it is about fictional amoeba, not mathematical amoeba :P
Dec 14 at 12:36	comment	added	M.G.		I thought for a second there that the post was about tropical geometry :-)
Dec 14 at 12:30	history	edited	Nate River	CC BY-SA 4.0	added 77 characters in body
Dec 14 at 12:20	history	edited	Nate River	CC BY-SA 4.0	added 55 characters in body
Dec 14 at 12:13	history	edited	Nate River	CC BY-SA 4.0	added 88 characters in body
Dec 14 at 12:08	history	asked	Nate River	CC BY-SA 4.0