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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 polynomialof a random matrix; relating the random matrix problem to another problem fromstatistical mechanics; and applying a heuristic analysis of that problem.  In this note we recover a conjecture like that of Fyodorov and Keating, butusing a different model for $|\zeta(1/2+it)|$ in terms of a random Eulerproduct. In this case the probabilistic model reduces to studying the supremumof Gaussian random variables with logarithmic correlations, and can be analysedrigorously.

A note on the maximum of the Riemann zeta function, and log-correlated random variables