  Georgiou, Katkov and Tsodyks considered the following random process. Let
$x_1,x_2,\ldots $ be an infinite sequence of independent, identically
distributed, uniform random points in $[0,1]$. Starting with $S=\{0\}$, the
elements $x_k$ join $S$ one by one, in order. When an entering element is
larger than the current minimum element of $S$, this minimum leaves $S$. Let
$S(1,n)$ denote the content of $S$ after the first $n$ elements $x_k$ join.
Simulations suggest that the size $|S(1,n)|$ of $S$ at time $n$ is typically
close to $n/e$. Here we first give a rigorous proof that this is indeed the
case, and that in fact the symmetric difference of $S(1,n)$ and the set
$\{x_k\ge 1-1/e: 1 \leq k \leq n \}$ is of size at most $\tilde{O}(\sqrt n)$
with high probability. Our main result is a more accurate description of the
process implying, in particular, that as $n$ tends to infinity $ n^{-1/2}\big(
|S(1,n)|-n/e \big) $ converges to a normal random variable with variance
$3e^{-2}-e^{-1}$. We further show that the dynamics of the symmetric difference
of $S(1,n)$ and the set $\{x_k\ge 1-1/e: 1 \leq k \leq n \}$ converges with
proper scaling to a three dimensional Bessel process.
