Abstract
For a natural extension of the circular unitary ensemble of order $\mathit{n}$, we study as $\mathit{n} \to \infty$ the asymptotic behavior of the sequence of monic orthogonal polynomials ($\Phi_{\mathit{k,n}}$, $\mathit{k}$ = 0, … ,$\mathit{n}$) with respect to the spectral measure associated with a fixed vector, the last term being the characteristic polynomial. We show that, $\mathit{n} \to \infty$ , the sequence of processes (log $\Phi_{\llcorner\mathit{nt}\lrcorner, \mathit{n}}$ (1), $\mathit{t} \in$ [0,1]) converges to a deterministic limit, and we describe the fluctuations and the large deviations.
Najnudel, Joseph