Publications

Preprints

  • Fredholm determinant solutions to the modified KP hierarchy and 2D Toda lattice: isospectral and non-isospectral reductions
    D. Dai, H.-H. Sheng
    preprint — [arXiv:2609.37421]
  • Asymptotics of Hankel determinants for potentials with singular edge points
    D. Dai, J.-H. Du, C. Lu
    preprint — [arXiv:2609.26412]
  • On the eigenvalue rigidity of the Jacobi unitary ensemble
    D. Dai, C. Lu
    preprint — [arXiv:2511.18967]
  • The multiplicative constant in asymptotics of higher-order analogues of the Tracy-Widom distribution
    D. Dai, W.-G. Long, S.-X. Xu, L.-M. Yao, L. Zhang
    SIAM Journal on Mathematical Analysis, to appear. — [arXiv:2501.12679]

Published Papers

  • Nonisospectral deformations of noncommutative Laurent biorthogonal polynomials and matrix discrete Painlevé-type equations
    D. Dai, X. Yue
    Studies in Applied Mathematics, 157 (2026), no. 3, e70251. — [arXiv:2510.27402]
  • Orthogonal polynomials with periodic recurrence coefficients
    D. Dai, M.E.H. Ismail, X.-S. Wang
    Analysis and Applications, 24 (2026), no. 4, 937-961. — [arXiv:2412.08166]
  • A note on inequalities for Gaussian hypergeometric functions
    D. Dai, T. Sang
    Journal of Mathematical Inequalities, 19 (2025), no. 2, 707-715.
  • Asymptotics of the confluent hypergeometric process with a varying external potential in the super-exponential region
    D. Dai, L. Yao, Y. Zhai
    Analysis and Applications, 22 (2024), no. 8, 1353-1387. — [arXiv:2403.16475]
  • Asymptotics and total integrals of the PI2 tritronquée solution and its Hamiltonian
    D. Dai, W.-G. Long
    SIAM Journal on Mathematical Analysis, 56 (2024), no. 4, 5350-5371. — [arXiv:2306.15847]
  • From continuous to discrete: weak limit of normalized Askey-Wilson measure
    D. Dai, M.E.H. Ismail, X.-S. Wang
    The Ramanujan Journal, 64 (2024), no. 1, 227-252.
  • Gap probability for the hard edge Pearcey process
    D. Dai, S.-X. Xu, L. Zhang
    Annales Henri Poincaré, 24 (2023), no. 6, 2067-2136.— [arXiv:2204.04625]
  • The distribution function for the maximal height of N non-intersecting Bessel paths
    D. Dai, L. Yao
    The Ramanujan Journal, 61 (2023), no. 1, 111-134.— [arXiv:1908.00736]
  • Asymptotics of the deformed Fredholm determinant of the confluent hypergeometric kernel
    D. Dai, Y. Zhai
    Studies in Applied Mathematics, 149 (2022), no. 4, 1032-1085.— [arXiv:2205.03897]
  • Uniform asymptotics for the discrete Laguerre polynomials
    D. Dai, L. Yao
    Analysis and Applications, 20 (2022), no. 5, 1025-1067.— [arXiv:2104.03563]
  • Applications in random matrix theory of a PIII′ τ-function sequence from Okamoto's Hamiltonian formulation
    D. Dai, P.J. Forrester, S.-X. Xu
    Random Matrices: Theory and Applications, 11 (2022), no. 2, Paper No. 2250014, 20 pp.— [arXiv:1909.07634]
  • On the deformed Pearcey determinant
    D. Dai, S.-X. Xu, L. Zhang
    Advances in Mathematics, 400 (2022), Paper No. 108291, 64 pp. — [arXiv:2007.12691]
  • Asymptotics of Fredholm determinant associated with the Pearcey kernel
    D. Dai, S.-X. Xu, L. Zhang
    Communications in Mathematical Physics, 382 (2021), 1769-1809. — [arXiv:2002.06370]
  • On integrals of the tronquée solutions and the associated Hamiltonians for the Painlevé II equation
    D. Dai, S.-X. Xu, L. Zhang
    Journal of Differential Equations, 269 (2020), no. 3, 2430-2476.— [arXiv:1908.01532]
  • Asymptotics of orthogonal polynomials with asymptotic Freud-like weights
    W.-G. Long, D. Dai, Y.-T. Li, X.-S. Wang
    Studies in Applied Mathematics, 144 (2020), no. 2, 133-163.
  • On a Ramanujan type entire function and its zeros
    D. Dai, M.E.H. Ismail, X.-S. Wang
    Journal of Mathematical Analysis and Applications, 485 (2020), no. 2, 123856, 16 pp.
  • Gaussian unitary ensembles with pole singularities near the soft edge and a system of coupled Painlevé XXXIV equations
    D. Dai, S.-X. Xu, L. Zhang
    Annales Henri Poincaré, 20 (2019), no. 10, 3313-3364.— [arXiv:1809.07074]
  • Tracy-Widom distributions in critical unitary random matrix ensembles and the coupled Painlevé II system
    S.-X. Xu, D. Dai
    Communications in Mathematical Physics, 365 (2019), no. 2, 515-567. — [arXiv:1708.06113]
  • Asymptotics of partition functions in a fermionic matrix model and of related q-polynomials
    D. Dai, M.E.H. Ismail, X.-S. Wang
    Studies in Applied Mathematics, 142 (2019), no. 1, 91-105.— [arXiv:1808.01193]
  • Doubly infinite Jacobi matrices revisited: resolvent and spectral measure
    D. Dai, M.E.H. Ismail, X.-S. Wang
    Advances in Mathematics, 343 (2019), 157-192.
  • On the quasi-Ablowitz-Segur and quasi-Hastings-McLeod solutions of the inhomogeneous Painlevé II equation
    D. Dai, W. Hu
    Random Matrices: Theory and Applications, 7 (2018), no. 4, 1840004, 13 pp.— [arXiv:1708.09357]
  • Asymptotics of orthogonal polynomials and the Painlevé transcendents
    D. Dai
    Frontiers in Orthogonal Polynomials and q-Series, Contemporary Mathematics and Its Applications: Monographs, Expositions and Lecture Notes, Vol. 1, World Scientific Publishing, (2018), 189-212.— [arXiv:1608.04513]
  • Gap probability at the hard edge for random matrix ensembles with pole singularities in the potential
    D. Dai, S.-X. Xu, L. Zhang
    SIAM Journal on Mathematical Analysis, 50 (2018), no. 2, 2233-2279. — [arXiv:1710.08132]
  • Connection formulas for the Ablowitz-Segur solutions of the inhomogeneous Painlevé II equation
    D. Dai, W. Hu
    Nonlinearity, 30 (2017), no. 7, 2982-3009.— [arXiv:1611.05285]
  • Hankel determinants for a singular complex weight and the first and third Painlevé transcendents
    S.-X. Xu, D. Dai, Y.-Q. Zhao
    Journal of Approximation Theory, 205 (2016), 64-92.— [arXiv:1509.07015]
  • Uniform asymptotics of orthogonal polynomials arising from coherent states
    D. Dai, W. Hu, X.-S. Wang
    SIGMA. Symmetry, Integrability and Geometry: Methods and Applications, 11 (2015), Paper 070, 17 pp.— [arXiv:1408.5654]
  • Asymptotics for Laguerre polynomials with large order and parameters
    D. Dai, M.E.H. Ismail, J. Wang
    Journal of Approximation Theory, 193 (2015), 4-19.
  • Painlevé III asymptotics of Hankel determinants for a singularly perturbed Laguerre weight
    S.-X. Xu, D. Dai, Y.-Q. Zhao
    Journal of Approximation Theory, 192 (2015), 1-18.— [arXiv:1407.7334]
  • Critical edge behavior and the Bessel to Airy transition in the singularly perturbed Laguerre unitary ensemble
    S.-X. Xu, D. Dai, Y.-Q. Zhao
    Communications in Mathematical Physics, 332 (2014), no. 3, 1257-1296. — [arXiv:1309.4354]
  • Uniform asymptotics for orthogonal polynomials with exponential weight on the positive real axis
    D. Dai, W. Qiu, J. Wang
    Asymptotic Analysis, 89 (2014), no. 1-2, 1-19.
  • Plancherel-Rotach asymptotic expansion for some polynomials from indeterminate moment problems
    D. Dai, M.E.H. Ismail, X.-S. Wang
    Constructive Approximation, 40 (2014), no. 1, 61-104.— [arXiv:1302.6196]
  • Existence and uniqueness of tronquée solutions of the third and fourth Painlevé equations
    Y. Lin, D. Dai, P. Tibboel
    Nonlinearity, 27 (2014), no. 2, 171-186.— [arXiv:1306.1317]
  • Asymptotics of the partition function of a Laguerre-type random matrix model
    Y. Zhao, L. H. Cao, D. Dai
    Journal of Approximation Theory, 178 (2014), 64-90.— [arXiv:1304.4782]
  • Painlevé V and a Pollaczek-Jacobi type orthogonal polynomials
    Y. Chen, D. Dai
    Journal of Approximation Theory, 162 (2010), no. 12, 2149-2167.— [arXiv:0809.3641]
  • On tronquée solutions of the first Painlevé hierarchy
    D. Dai, L. Zhang
    Journal of Mathematical Analysis and Applications, 368 (2010), no. 2, 393-399.
  • Painlevé VI and Hankel determinants for the generalized Jacobi weight
    D. Dai, L. Zhang
    Journal of Physics A: Mathematical and Theoretical, 43 (2010), no. 5, 055207, 14 pp.— [arXiv:0908.0558]
  • Painlevé IV asymptotics for orthogonal polynomials with respect to a modified Laguerre weight
    D. Dai, A.B.J. Kuijlaars
    Studies in Applied Mathematics, 122 (2009), no. 1, 29-83.— [arXiv:0804.2564]
  • Global asymptotics for Laguerre polynomials with large negative parameter—a Riemann-Hilbert approach
    D. Dai, R. Wong
    The Ramanujan Journal, 16 (2008), no. 2, 181-209.
  • Global asymptotics of Krawtchouk polynomials—a Riemann-Hilbert approach
    D. Dai, R. Wong
    Chinese Annals of Mathematics, Series B, 28 (2007), no. 1, 1-34.

Books Edited

  • The selected works of Roderick S. C. Wong. Vol. 4.
    Editors: D. Dai, D.-X. Zhou
    World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2026.
  • The selected works of Roderick S. C. Wong. Vol. 1, 2, 3.
    Editors: D. Dai, H.-H. Dai, T. Yang, D.-X. Zhou
    World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2016.