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For a random binary noncoalescing feedback shift register of width $n$, withall $2^{2^{n-1}}$ possible feedback functions $f$ equally likely, the processof long cycle lengths, scaled by dividing by $N=2^n$, converges in distributionto the same Poisson-Dirichlet limit as holds for random permutations in$\mathcal{S}_N$, with all $N!$ possible permutations equally likely. Suchbehavior was conjectured by Golomb, Welch, and Goldstein in 1959.

Random Feedback Shift Registers, and the Limit Distribution for Largest Cycle Lengths