I am an associate professor and docent at the Department of Mathematics at KTH Royal Institute of Technology. My research interests are in Probability Theory, Mathematical Statistics and Mathematical Physics, with a focus on Random Matrix Theory and Free Probability. My research is supported by the Knut and Alice Wallenberg Foundation and the Swedish Research Council (Grants VR-2017-05195, VR-2021-04703).

Together with Maurice Duits and Kurt Johansson, I am part of the focus group Random Matrices, Stochastic Models and Analysis within the Department of Mathematics at KTH.

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Contact

Email:		schnelli at kth dot se
Address:		KTH Department of Mathematics Lindstedtsvägen 25 SE-100 44 Stockholm Sweden
Office:		3639 on 6th floor
Maps:		Campus map (pdf) Google maps

Current teaching

• Differentialequations with Applications SF1676 (Spring 22, examiner & course responsible)
• Probability Theory SF2940 (Fall 22, examiner & course responsible)

Publications and preprints

1. Asymptotic freeness through unitaries generated by polynomials of Wigner matrices
   with Félix Parraud
   preprint, arXiv:2208.02118 (2022).
2. Quantitative Tracy-Widom laws for the largest eigenvalue of generalized Wigner matrices
   with Yuanyuan Xu
   preprint, arXiv:2207.00546 (2022).
3. The support of the free additive convolution of multi-cut measures
   with Philippe Moreillon
   preprint, arXiv:2201.05582 (2022).
4. Convergence rate to the Tracy-Widom laws for the largest eigenvalue of Wigner matrices
   with Yuanyuan Xu
   to appear in Ann. Appl. Probab (2021).
5. Convergence rate to the Tracy-Widom laws for the largest eigenvalue of Wigner matrices
   with Yuanyuan Xu
   Comm. Math. Phys. 393, 839-907 (2022).
6. Central limit theorem for mesoscopic eigenvalue statistics of the free sum of matrices
   with Zhigang Bao and Yuanyuan Xu
   Int. Math. Res. Not. IMRN 2022(7), 5320–5382 (2022).
7. Equipartition principle for Wigner matrices
   with Zhigang Bao and László Erdős
   Forum Math. Sigma 9e44, 1–21 (2021).
8. Central limit theorem for mesoscopic eigenvalue statistics of deformed Wigner matrix
   with Yiting Li and Yuanyuan Xu
   Ann. Inst. Henri Poincaré Probab. Stat. 57(1), 506-546 (2021).
9. On the support of the free additive convolution
   with Zhigang Bao and László Erdős
   J. Anal. Math. 142 , 323-348 (2020)
10. Spectral rigidity for addition of random matrices at the regular edge
    with Zhigang Bao and László Erdős
    J. Funct. Anal. 279(5) , 108639 (2020)
11. Local law and Tracy-Widom limit for sparse sample covariance matrices
    with Jong Yun Hwang and Ji Oon Lee
    Ann. Appl. Probab. 29(5), 3006-3036 (2019)
12. Local single ring theorem on optimal scale
    with Zhigang Bao and László Erdős
    Ann. Probab. 47(3), 1270-1334 (2019)
13. Local law and Tracy-Widom limit for sparse random matrices
    with Ji Oon Lee
    Probab. Theory Related Fields 171(1), 543-616 (2018)
14. Universality for random matrix flows with time-dependent density
    with László Erdős
    Ann. Inst. Henri Poincaré Probab. Stat. 53(4), 1606-1656 (2017)
15. Convergence rate for spectral distribution of addition of random matrices
    with Zhigang Bao and László Erdős
    Adv. Math. 319, 251-291 (2017)
16. Local law of addition of random matrices on optimal scale
    with Zhigang Bao and László Erdős
    Comm. Math. Phys. 349(3), 947-990 (2017)
17. Tracy-Widom distribution for the largest eigenvalue of real sample covariance matrices with general population
    with Ji Oon Lee
    Ann. Appl. Probab. 26(6), 3786-3839 (2016)
18. Local stability of the free additive convolution
    with Zhigang Bao and László Erdős
    J. Funct. Anal. 271(3), 672-719 (2016)
19. Bulk universality for deformed Wigner matrices
    with Ji Oon Lee, Ben Stetler and Horng-Tzer Yau
    Ann. Probab. 44(3), 2349-2425 (2016)
20. Extremal eigenvalues and eigenvectors of deformed Wigner matrices
    with Ji Oon Lee
    Probab. Theory Related Fields 164(1), 165-241 (2016)
21. Edge universality for deformed Wigner matrices
    with Ji Oon Lee
    Rev. Math. Phys. 27(8), 1550018 (2015)
22. Quantum diffusion with drift and the Einstein relation. II
    with Wojciech De Roeck and Jürg Fröhlich
    J. Math. Phys. 55, 075207 (2014)
23. Quantum diffusion with drift and the Einstein relation. I
    with Wojciech De Roeck and Jürg Fröhlich
    J. Math. Phys. 55, 075206 (2014)
24. Local deformed semicircle law and complete delocalization for Wigner matrices with random potential
    with Ji Oon Lee
    J. Math. Phys. 54, 103504 (2013)

Education and employment

Since July 2020		Associate Professor at Department of Mathematics KTH Royal Institute of Technology
Oct. 2018:		Docent in Mathematics, KTH Royal Institute of Technology
2016‒2020		Assistant Professor tenure track at Department of Mathematics KTH Royal Institute of Technology
2014‒2016:		Post-doc at IST Austria
2013‒2014:		Member School of Mathematics, Institute for Advanced Study
2011‒2013:		Post-doc at Department of Mathematics, Harvard University
2007‒2011:		Ph.D. in theoretical Physics, ETH Zürich
2005‒2007:		M.Sc. in Physics, ETH Zürich
2002‒2005:		B.Sc. in Physics, EPF Lausanne

Links

• Focus group Random Matrices, Stochastic Models and Analysis
• Conference Random Matrices and Beyond A conference in celebration of Kurt Johansson's 60th birthday, June 6-10, 2022.
• KTH Mathematics Calendar
  
• Seminars at KTH: Random Matrix Theory.
• Seminars at AlbaNova University Center: Weekly schedule
• Studying at KTH: Ph.D. programs in mathematics; M.Sc. program in mathematics, joint with Stockholm University SU at Stockholm Mathematics Center SMC
• Not far from KTH: AlbaNova, Stockholm University, Institut Mittag-Leffler, Uppsala University
• Practical matters: SL start page; closest subway station: Tekniska högskolan (line T-14).