Asymptotics of the largest eigenvalue distribution of the Laguerre unitary ensemble

@article{Lyu2015AsymptoticsOT,
  title={Asymptotics of the largest eigenvalue distribution of the Laguerre unitary ensemble},
  author={Shulin Lyu and Chao Min and Yang Chen},
  journal={Journal of Mathematical Physics},
  year={2015}
}
We study the probability that all eigenvalues of the Laguerre unitary ensemble of n by n matrices are between 0 and t, i.e., the largest eigenvalue distribution. Associated with this probability, in the ladder operator approach for orthogonal polynomials, there are recurrence coefficients, namely {\alpha}n(t) and \b{eta}n(t), as well as three auxiliary quantities, denoted by rn(t), Rn(t) and sigma n(t). We establish the second order differential equations for both beta n(t) and rn(t). By… 

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