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We introduce a family of discrete determinantal point processes related to orthogonal polynomials on the real line, with correlation kernels defined via spectral projections for the associated Jacobi matrices.
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C. Tracy and H. Widom, Asymptotics in ASEP with step initial condition. Comm. Math. Phys. 290 (2009), 129–154
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N. O’Connell, Directed polymers and the quantum Toda lattice, Ann. Probab. 40, no. 2 (2012), 437–458
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T. Tao, Topics in random matrix theory. Graduate Studies in Mathematics, vol. 132. Amer. Math. Soc., 2012
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