Journal of Theoretical Probability

, Volume 29, Issue 4, pp 1199–1239 | Cite as

Limit Theorems for Orthogonal Polynomials Related to Circular Ensembles

  • Joseph Najnudel
  • Ashkan Nikeghbali
  • Alain RouaultEmail author


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


Random matrices Unitary ensemble Orthogonal polynomials  Large deviation principle Invariance principle 

Mathematics Subject Classification (2010)

15B52 42C05 60F10 60F17 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Joseph Najnudel
    • 1
  • Ashkan Nikeghbali
    • 2
  • Alain Rouault
    • 3
    Email author
  1. 1.Institut de Mathématiques de ToulouseUniversité Paul SabatierToulouse Cedex 9France
  2. 2.Institut für MathematikUniversität ZürichZürichSwitzerland
  3. 3.Université Versailles-Saint Quentin, LMV, Bâtiment FermatVersailles CedexFrance

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