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 VR201705195, VR202104703).
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.
Contact
Email:  schnelli at kth dot se  
Address:  KTH Department of Mathematics Lindstedtsvägen 25 SE100 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

Asymptotic freeness through unitaries generated by polynomials of Wigner matrices
with Félix Parraud
preprint, arXiv:2208.02118 (2022). 
Quantitative TracyWidom laws for the largest eigenvalue of generalized Wigner matrices
with Yuanyuan Xu
preprint, arXiv:2207.00546 (2022). 
The support of the free additive convolution of multicut measures
with Philippe Moreillon
preprint, arXiv:2201.05582 (2022). 
Convergence rate to the TracyWidom laws for the largest eigenvalue of Wigner matrices
with Yuanyuan Xu
to appear in Ann. Appl. Probab (2021). 
Convergence rate to the TracyWidom laws for the largest eigenvalue of Wigner matrices
with Yuanyuan Xu
Comm. Math. Phys. 393, 839907 (2022). 
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). 
Equipartition principle for Wigner matrices
with Zhigang Bao and László Erdős
Forum Math. Sigma 9e44, 1–21 (2021). 
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), 506546 (2021). 
On the support of the free additive convolution
with Zhigang Bao and László Erdős
J. Anal. Math. 142 , 323348 (2020) 
Spectral rigidity for addition of random matrices at the regular edge
with Zhigang Bao and László Erdős
J. Funct. Anal. 279(5) , 108639 (2020) 
Local law and TracyWidom limit for sparse sample covariance matrices
with Jong Yun Hwang and Ji Oon Lee
Ann. Appl. Probab. 29(5), 30063036 (2019) 
Local single ring theorem on optimal scale
with Zhigang Bao and László Erdős
Ann. Probab. 47(3), 12701334 (2019) 
Local law and TracyWidom limit for sparse random matrices
with Ji Oon Lee
Probab. Theory Related Fields 171(1), 543616 (2018) 
Universality for random matrix flows with timedependent density
with László Erdős
Ann. Inst. Henri Poincaré Probab. Stat. 53(4), 16061656 (2017) 
Convergence rate for spectral distribution of addition of random matrices
with Zhigang Bao and László Erdős
Adv. Math. 319, 251291 (2017) 
Local law of addition of random matrices on optimal scale
with Zhigang Bao and László Erdős
Comm. Math. Phys. 349(3), 947990 (2017) 
TracyWidom distribution for the largest eigenvalue of real sample covariance matrices with general population
with Ji Oon Lee
Ann. Appl. Probab. 26(6), 37863839 (2016) 
Local stability of the free additive convolution
with Zhigang Bao and László Erdős
J. Funct. Anal. 271(3), 672719 (2016) 
Bulk universality for deformed Wigner matrices
with Ji Oon Lee, Ben Stetler and HorngTzer Yau
Ann. Probab. 44(3), 23492425 (2016) 
Extremal eigenvalues and eigenvectors of deformed Wigner matrices
with Ji Oon Lee
Probab. Theory Related Fields 164(1), 165241 (2016) 
Edge universality for deformed Wigner matrices
with Ji Oon Lee
Rev. Math. Phys. 27(8), 1550018 (2015) 
Quantum diffusion with drift and the Einstein relation. II
with Wojciech De Roeck and Jürg Fröhlich
J. Math. Phys. 55, 075207 (2014) 
Quantum diffusion with drift and the Einstein relation. I
with Wojciech De Roeck and Jürg Fröhlich
J. Math. Phys. 55, 075206 (2014) 
Local deformed semicircle law and complete delocalization for Wigner matrices with random potential
with Ji Oon Lee
J. Math. Phys. 54, 103504 (2013)
My papers on arXiv.
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:  Postdoc at IST Austria  
2013‒2014:  Member School of Mathematics, Institute for Advanced Study  
2011‒2013:  Postdoc 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 610, 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 MittagLeffler, Uppsala University
 Practical matters: SL start page; closest subway station: Tekniska högskolan (line T14).
Updated last: September 1, 2022.