  In recent work, Fyodorov and Keating conjectured the maximum size of
$|\zeta(1/2+it)|$ in a typical interval of length O(1) on the critical line.
They did this by modelling the zeta function by the characteristic polynomial
of a random matrix; relating the random matrix problem to another problem from
statistical mechanics; and applying a heuristic analysis of that problem.
  In this note we recover a conjecture like that of Fyodorov and Keating, but
using a different model for $|\zeta(1/2+it)|$ in terms of a random Euler
product. In this case the probabilistic model reduces to studying the supremum
of Gaussian random variables with logarithmic correlations, and can be analysed
rigorously.
