Samples of algebraic central limit theorems based on \(\mathbb{Z}/2\mathbb{Z}\) (Q2751510)

Let \(\sigma_1,\dots, \sigma_N\) be the canonical generators of the group \((\mathbb{Z}/2\mathbb{Z})^N\). It is well-known that the spectrum of \((\sigma_1+\cdots+ \sigma_N)/\sqrt{N}\) converges for \(N\to\infty\) to the Wigner semicircle law where the limit has some Fock representation. In this paper, the author gives similar results for \(\sum_{1\leq i\neq j\leq N}\sigma_i \sigma_j/\sqrt{N(N- 1)}\) as well as for the sums of triple products of the same kind. This result for multi-foldings of free elements may be interpreted as a conditionally free, but not free central limit theorem.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00042].