Maximum possible reputation? (NOT a meta question) I had the following idea about the reputation system of MSE, that led to a math question:

Suppose a certain user on MSE gains an average of $+200$ reputation per day - the daily maximum. Suppose that this reputation comes from one vote from each of $20$ randomly selected (not necessarily distinct) users on the site each day. Then it seems that, at some point, this "superuser" would reach a sort of equilibrium by losing $200$ reputation each day just from other users who had previously upvoted her being deleted. Would this happen, or would the superuser grow in reputation unboundedly? If she is expected to top off, at what reputation would she stagnate?

To answer this question, one would need to use some of the statistics from this site, such as the average user deletion rate, average number of users at any time, and so on. I don't expect to find a perfect answer, but a pretty good estimate should be obtainable.

I believe that your reputation will tend to infinity.
By the way, 200 is not the maximum reputation gain in a day; points from acceptances and bounties don't count toward the cap, and are unlimited. But that doesn't matter because I'm not assuming that you're maxing out your daily reputation gains. I only assume that your net reputation change (not counting deletions) is positive, i.e., you're gaining more points from upvotes etc. than you're losing to downvotes.
It is my understanding that death is not a cause for deleting a user's account. Therefore, anyone who manages to die (or become permanently inactive for any other reason) in a "state of grace" with Stack Exchange, will never be deleted.
Some of your votes come from "mortal" users, who are fated to be deleted someday; and some of them come from "immortal" users, who will never be deleted. Your accumulated reputation score at any time will be the sum of your "immortal" votes (which clearly grows to infinity) plus the current population of "mortal" votes (which fluctuates unpredictably). Q.E.D.
