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We apply realization theory of non-commutative rational multipliers of theFock space, or free Hardy space of square--summable power series in severalnon-commuting variables to the convex analysis of states on the Cuntz algebra.We show, in particular, that a large class of Cuntz states which arise as the`non-commutative Clark measures' of isometric NC rational multipliers are peakstates for Popescu's free disk algebra in the sense of Clou\^atre and Thompson.

Rational Cuntz states peak on the free disk algebra