Abstract :
The cyclic corrections (i.e. the contribution of cyclic particle exchanges) to the anyon partition functions are computed at all perturbative orders of the statistical coupling in the thermodynamic limit. A possible generalization for anyons in a harmonic well is revisited. One shows that this proposal correctly encompasses the contribution of the linear energies both in the symmetric, antisymmetric and mixed representations, but it is not satisfying as regards the contribution of the non-linear energies. Finally, one builds a few-body spectrum which interpolates linearly between the Bose one and the Fermi one in a harmonic well, it reproduces the previous proposal, and it is consistent with a finite virial expansion where only the second coefficient is affected by the statistics in the thermodynamic limit.
