# Anyonic Partition Functions and Windings of Planar Brownian Motion

### Jean Desbois 1, Christine Heinemann 1, Stephane Ouvry 1

#### Physical Review D 51 (1995) 942-945

The computation of the $N$-cycle brownian paths contribution $F_N(\\alpha)$ to the $N$-anyon partition function is adressed. A detailed numerical analysis based on random walk on a lattice indicates that $F_N^{(0)}(\\alpha)= \\prod_{k=1}^{N-1}(1-{N\\over k}\\alpha)$. In the paramount $3$-anyon case, one can show that $F_3(\\alpha)$ is built by linear states belonging to the bosonic, fermionic, and mixed representations of $S_3$.

• 1. Division de Physique Théorique, IPN,
Université Paris XI - Paris Sud