Erratum to: Canonical Moments and Random Spectral Measures

Erratum to: J Theor Probab (2010) 23:1015–1038 DOI 10.1007/s10959-009-0239-1

The aim of this short note is to report a mistake in a power appearing in a Jacobian in [2, Lemma 3.3]. Notice that this result and mistake occurred earlier in [3, Lemma 7.3]. Indeed, the error comes from a wrong Jacobian computation: If $z,w \in \mathbb C$ with $z=x+iy$, $w=s+it$ $(x,y,s,t\in \mathbb R)$ and $k>0$ with $z=kw$, then the Jacobian $\displaystyle \left| \frac{D(x,y)}{D(s,t)}\right|$ equals $k^2$ and not k (in brief, $d^2z$ equals $k^2 d^2 w$ and not $k d^2w$). The correct density of $c_j$ is then $\eta _{2(N-j)}$. Consequently, Theorem 4.1 and Corollary 4.2 of [2] are invalidated.

The previous mistake is also reported in the remark at the beginning of Section 4.2 of [1].