Semi-Poisson statistics and beyond.

Semi-Poisson statistics are shown to be obtained by removing every other number from a random sequence. Retaining every (r+1)th level we obtain a family of sequences, which we call daisy models. Their statistical properties coincide with those of Bogomolny's nearest-neighbor interaction Coulomb gas if the inverse temperature coincides with the integer r. In particular, the case r=2 reproduces closely the statistics of quasioptimal solutions of the traveling salesman problem.