Dominik Schröder

After obtaining my PhD in 2019 under the supervision of László Erdős at the Institute of Science and Technology Austria, I have been a junior fellow at the ETH Institute for Theoretical Studies since September 2019. My research interests are probability theory and mathematical physics with a focus on random matrices. I am also interested in universal properties of complex systems and the mathematically rigorous study of machine learning algorithms.

Curriculum vitae

  • 2010 – 2011. BSc, ETH Zurich
  • 2011 – 2014. BSc and MSc, LMU Munich
  • 2014 – 2015. MASt, University of Cambridge, Clare College
  • 2015 – 2019. PhD, IST Austria
  • 04 – 08/2018. Industry Sabbatical, Bosch Center for Artificial Intelligence
  • since 09/2019. Junior Fellow, Institute for Theoretical Studies, ETH Zurich

Curriculum vitae (pdf) for more detailed information.

Theses

  • PhD Thesis From Dyson to Pearcey: Universal Statistics in Random Matrix Theory for a PhD in Mathematics supervised by László Erdős
  • MSc Thesis Phase Transition in the Density of States of Quantum Spin Glasses for the MSc in Theoretical and Mathematical Physics supervised by László Erdős
  • Essay Interlacing Families and the Kadison–Singer Problem for the Master of Advanced Studies in Mathematics supervised by Timothy Gowers
  • BSc Thesis Integrated Density of States of Random Schrödinger Operators with Alloy-Type Potential for the BSc in Mathematics supervised by Peter Müller

Publications

All my publications can be found on the arXiv, on Google Scholar and on the MathSciNet.

  1. Phase Transition in the Density of States of Quantum Spin Glasses
    with László Erdős (2014)
    Math. Phys. Anal. Geom. 17 (2014), no. 3-4, 441–464.
    arXiv:1407.1552, MR3291938, doi:10.1007/s11040-014-9164-3

  2. Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues
    with László Erdős (2016)
    Int. Math. Res. Not. IMRN 2018, no. 10, 3255–3298.
    arXiv:1608.05163, MR3805203, doi:10.1093/imrn/rnw330

  3. Fluctuations of Functions of Wigner Matrices
    with László Erdős (2016)
    Electron. Commun. Probab. Volume 21 (2016), paper no. 86, 15 pp.
    arXiv:1610.07084, MR3600514, doi:10.1214/16-ECP38

  4. Random Matrices with Slow Correlation Decay
    with László Erdős and Torben Krüger (2017)
    Forum of Mathematics, Sigma, 7, E8 (2019).
    arXiv:1705.10661, MR3941370, doi:10.1017/fms.2019.2

  5. Correlated Random Matrices: Band Rigidity and Edge Universality
    with Johannes Alt, László Erdős and Torben Krüger (2018)
    Ann. Probab. 48 (2020), no. 2, 963–1001.
    arXiv:1804.07744, MR4089499, doi:10.1214/19-AOP1379

  6. Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case
    with László Erdős and Torben Krüger (2018)
    Comm. Math. Phys. 378 (2020), no. 2, 1203–1278.
    arXiv:1809.03971, MR4134946, doi:10.1007/s00220-019-03657-4

  7. Cusp Universality for Random Matrices II: The Real Symmetric Case
    with Giorgio Cipolloni, László Erdős and Torben Krüger (2018)
    Pure Appl. Anal. 1 (2019), no. 4, 615–707.
    arXiv:1811.04055, MR4026551, doi:10.2140/paa.2019.1.615

  8. Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble
    with Giorgio Cipolloni and László Erdős (2019)
    Probability and Mathematical Phsyics Vol. 1 (2020), No. 1, 101–146.
    arXiv:1908.01653, doi:10.2140/pmp.2020.1.101

  9. Edge Universality for non-Hermitian Random Matrices
    with Giorgio Cipolloni and László Erdős (2019)
    Probab. Theory Relat. Fields (2020).
    arXiv:1908.00969, doi:10.1007/s00440-020-01003-7

  10. Central Limit Theorem for Linear Eigenvalue Statistics of non-Hermitian Random Matrices
    with Giorgio Cipolloni and László Erdős (2019)
    accepted for publication in Comm. Pure Appl. Math.
    arXiv:1912.04100

  11. Fluctuation Around the Circular Law for Random Matrices with Real Entries
    with Giorgio Cipolloni and László Erdős (2020)
    preprint
    arXiv:2002.02438

  12. Eigenstate Thermalization Hypothesis for Wigner Matrices
    with Giorgio Cipolloni and László Erdős (2020)
    preprint
    arXiv:2012.13215

  13. Functional Central Limit Theorems for Wigner Matrices
    with Giorgio Cipolloni and László Erdős (2020)
    preprint
    arXiv:2012.13218

Teaching

Research Rotations

  1. Limits to gene regulation due to crosstalk.
    with Gašper Tkačik
    Internal report (2015)
  2. Analysing response of retinal neurons in fish and Generalization bounds for active task selection.
    with Christoph Lampert
    Internal report (2016)

Contact Information

ETH Zurich
Institute for Theoretical Studies
Clausiusstrasse 47
Building CLV
8092 Zurich

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