Research



Together with Kurt Johansson and Kevin Schnelli I am part on the focus group on "Random matrices, stochastics models and analysis" within the Mathematics Department at KTH. Click here for more details on our group and it activities.

I am currently receiving funding from the Swedish Research council grants VR-2012-3128 and VR-2016-05450, the Gustafsson Foundation and the Knut and Allice Wallenberg foundation.

Preprints

  • (with A. Kuijlaars), The two periodic Aztec diamond and matrix valued orthogonal polynomials (arXiv:1712.05636) ,

Published papers

  • (with R. Kozhan), Relative Szego Asymptotics for Toeplitz determinants, (arXiv:1611.01020) , accepted for publication in International Mathematics Research Notices
  • (with T. Berggren), Mesoscopic fluctuations for the thinned Circular Unitary Ensemble, (arXiv:1611.00991) , Mathematical physics, analysis and geometry, vol. 20, no. 3, 2017.
  • On global fluctuations for non-colliding processes, (arXiv:1510.08248) , accepted for publication in Annals of Probability, The Annals of Probability 2018, Vol. 46, No. 3, 1279–1350.
  • (with K. Johansson), On mesoscopic equilibrium for linear statistics in Dyson's Brownian Motion accepted for publication in Memoirs of the AMS (arXiv:1312.4295)
  • (with J. Breuer), Central Limit Theorems for biorthogonal ensembles and asymptotics of recurrence coefficients, J. Amer. Math. Soc. 30 (2017) No. 1, 27--66. (arXiv:1309.6224)
  • (with J. Breuer), Universality of mesocopic fluctuation in orthogonal polynomial ensembles, Comm. Math. Phys. 342 (2016), no. 2, 491--531. . (arXiv:1411.5205)
  • (with J. Breuer), The Nevai condition and a local law of large numbers for orthogonal polynomial ensembles,  Adv. Math. 265 (2014), 441--484. (arXiv:1301.2061)
  • Painlevé kernels in Hermitian matrix models, Constr. Approx. 39 (2014), No 1, 173--196 (arXiv:1302.1710)
  • (with D. Geudens), A critical phenomenon in the two-matrix model in the quartic/quadratic case, Duke Math. J. 162 (2013) No. 8, 1383--1462. (arXiv:1111.2162)
  • The Gaussian free field in an interlacing particle system with two jump rates,Comm. Pure and Appl. Math. 66 (2013), no. 4, 600--643. (arXiv:1105.4656)
  • (with A. Kuijlaars and M. Mo), Asymptotic analysis of the two matrix model with a quartic potential, To appear in Volume 65 of the MSRI book series (arXiv:1210.0097)
  • (with J. Breuer), Nonintersecting paths with a staircarse initial condition, Electron. J. Probab. 17 (2012), no. 60, 1--24. (arXiv:1105.0388)
  • (with A. Kuijlaars and M. Mo), The Hermitian two matrix model with an even quartic potential, Mem. Amer. Math. Soc. 217 (2012), no. 1022, 105 pp. (arXiv:1010.4282)
  • (with D. Geudens and A. Kuijlaars), A vector equilibrium problem for the two-matrix model in the quartic/quadratic case, Nonlinearity 24 (2011), 951--993. (arXiv:1007.3137)
  • (with A. Borodin), Limits of determinantal processes near a tacnode, Ann. Inst. Henri Poincare (B) 47 (2011), no. 1, 243-258. (arXiv:0911.1980)
  • (with S. Delvaux), An equilibrium problem for the limiting eigenvalue distribution of rational Toeplitz matrices, SIAM J. Matrix Anal. 31(4) (2010), 1894--1914. (arXiv:0911.4897)
  • (with K. Johansson), Powers of large random unitary matrices and Toeplitz determinants, Trans. Amer. Math. Soc. 362 (2010), 1169-1187. (math-ph/0607017)
  • (with A. Kuijlaars), Universality in the two matrix model: a Riemann-Hilbert steepest descent analysis, Comm. Pure Appl. Math. 62 (2009), 1076--1153. (arXiv:0807.4814)
  • (with A. Kuijlaars), An equilibrium problem for the limiting eigenvalue distribution of banded Toeplitz matrices, SIAM J. Matrix Anal. Appl. 30 (2008), 173--196.(arXiv:0704.0378)
  • (with A. Kuijlaars), Painlevé I asymptotics for orthogonal polynomials with respect to a varying quadratic weight, Nonlinearity 19 (2006), 2211-2245. (math.CA/0605201)

Teaching

Contact details

Mathematics Department
Royal Institute of Technology
Lindstedtsvägen 25
Stockholm SE-100044
Sweden

Office: 3733
Phone: +46 8 790 62 36
Email: duits at kth dot se