Thorsten Neuschel

I am an analyst and probabilist interested in asymptotics and high-dimensional problems arising from pure and applied mathematics and mathematical physics, where one main focus of my research is connected to the field of random matrix theory and the universality phenomena arising in these contexts. Furthermore, I am interested in academic and educational writing.

Brief Curriculum Vitae

• Since   2022:   Assisstant Professor for Mathematics at Dublin City University

• 2021 - 2022:   Deputy Professor for Stochastic Methods in Data Science at the Friedrich-Alexander University Erlangen-Nürnberg 

• 2018 - 2021:   Research Associate in the CRC Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications located at the University of Bielefeld

• 2018:               Habilitation in Mathematics with the thesis Analytic Studies of Average Characteristic Polynomials and Eigenvalues of Random Product Matrices

• 2015 - 2018:   Postdoctoral Researcher as Chargé de Recherche, a third-party fellowship and grant funded by the Belgian Research Foundation FNRS located at the University of Louvain-la-Neuve

• 2016:               Visiting Professorship in the Department of Mathematics of the KU Leuven

• 2013 - 2015:   Research Associate in the Department of Mathematics of the KU Leuven

• 2011:               Doctorate (Ph.D.) in Mathematics with the thesis Asymptotics for Ménage Polynomials at the University Trier

• 2009:               Diploma in Mathematics with the thesis Euler-Frobenius Numbers

• 2008 - 2013:   Research Associate in the Department of Mathematics of the University Trier

Research Papers 

1. Transition Analysis: From the Airy and Pearcey Kernels to the Sine Kernel (with Martin Venker), preprint, arXiv:2412.10596. 

2. Asymptotic Normality of Centroids of Random Polygons, preprint, arXiv:2407.06960.
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3. Boundary Asymptotics for Non-Intersecting Brownian Motions: Pearcey, Airy and a Transition (with Martin Venker), Nonlinearity 37 (2024) 035008 (47pp) .

4. Characteristic polynomials of products of Wigner matrices: finite-N results and Lyapunov universality (with Gernot Akemann und Friedrich Götze), Electron. Commun. Probab. 26, article no. 30, 1-13, 2021.

5. Critical Behavior of Non-Intersecting Brownian Motions (with Tom Claeys und Martin Venker), Communications in Mathematical Physics 378, 1501-1537, 2020.

6. Boundaries of Sine Kernel Universality for Gaussian Perturbations of Hermitian Matrices (with Tom Claeys und Martin Venker), Random Matrices: Theory and Applications 8 (3), 1950011, 2019.

7. Spectral Densities of Singular Values of Products of Gaussian and Truncated Unitary Random Matrices, Random Matrices: Theory and Applications 9 (4), 2050014, 2020.

8. Jacobi Polynomial Moments and Products of Random Matrices (with W. Gawronski und D. Stivigny), Proceedings of the AMS 144, 5251-5263, 2016.

9. Asymptotic Zero Distribution of Jacobi-Pineiro and Multiple Laguerre Polynomials (with W. Van Assche), Journal of Approximation Theory 205, 114-132, 2016.

10. Asymptotics for Characteristic Polynomials of Wishart Type Products of Complex Gaussian and Truncated Unitary Random Matrices (with D. Stivigny), Journal of Multivariate Analysis 147, 155-167, 2016.

11. On the Asymptotic Normality of the Legendre-Stirling Numbers of the Second Kind (with W. Gawronski und L. Littlejohn), European Journal of Combinatorics 49, 218-231, 2015.

12. Complete Monotonicity and Zeros of Sums of Squared Baskakov Functions (mit U. Abel und W. Gawronski), Applied Mathematics and Computation 258, 130-137, 2015.

13. A Note on Extended Binomial Coefficients, Journal of Integer Sequences 17, Article 14.10.4, 2014.

14. On a Conjecture on Sparse Binomial-type Polynomials by Brown, Dilcher and Manna (with W. Gawronski), Analysis and Applications 12, 511--522, 2014.

15. Plancherel-Rotach Formulae for Average Characteristic Polynomials of Products of Ginibre Random Matrices and the Fuss-Catalan Distribution, Random Matrices: Theory and Applications 3 (1), 1450003, 2014.

16. Apéry Polynomials and the Multivariate Saddle Point Method, Constructive Approximation 40, 487-507, 2014.

17. Asymptotics of Stirling and Chebyshev-Stirling Numbers of the Second Kind (with W. Gawronski und L. Littlejohn), Studies in Applied Mathematics 133, 1-17, 2014.

18. A New Proof of Stirling's Formula, American Mathematical Monthly 121, 350-352, 2014.

19. Binomial Polynomials (with W. Gawronski und U. Abel), Computational Methods and Function Theory 13, 163-180, 2013.

20. Euler-Frobenius Numbers (mit W. Gawronski), Integral Transforms and Special Functions 24, 817-830, 2013.

21. Asymptotics for Ménage Polynomials and Certain Hypergeometric Polynomials of Type 3_F_1, Journal of Approximation Theory 164, 981-1006, 2012.

22. A Uniform Version of Laplace's Method for Contour Integrals, Analysis 32, 121-135, 2012.

Grants and Honors

1. Research position and grant Chargé de Recherche fully funded by the Belgian Research Foundation FNRS (180.000 Euro) in 2015.

2. Travel grant funded by Belgian Research Foundation FWO in 2015.

3. Award for outstanding dissertations funded by Freundeskreis Trierer Universität in 2012.

Educational Publications

I contributed several Chapters to the two german textbooks Mathematisch für Anfänger (2009) and Mathematisch für fortgeschrittene Anfänger (2010) published in Spektrum Akademischer Verlag.

1. Lineare Gleichungssysteme, Kapitel 10 in Mathematisch für Anfänger 

2. Lineare Abbildungen und ihre darstellenden Matrizen, Kapitel 11 in Mathematisch für Anfänger 

3. Determinanten, Kapitel 12 in Mathematisch für Anfänger 

4. Diagonalisierbarkeit, Kapitel 13 in Mathematisch für Anfänger

5. Über Permanenten, Permutationen und Fixpunkte, Kapitel 16 in Mathematisch für fortgeschrittene Anfänger

Teaching

Dublin City University

• Course on Analysis I (MTH1032)

• Course on Calculus in Several Variables (MS205)

• Course on Geometry (MS302)

• Course on Mathematics for Economics and Business (MS136)

• Course on Mathematics for Enterprise Computing (MS115)

• Course on Mathematics for Economics (MS145)

Friedrich-Alexander University Erlangen-Nürnberg

• Course on Introduction to Random Matrix Theory

• Course on Stochastic Modelling (Stochastische Modellbildung)

• Seminar on Spin Glasses with Applications to Deep Learning 

• Seminar and Bachelorseminar on Markov-Chains and Applications 

Bielefeld University

• Course on Random Matrix Theory

• Co-organization of the international Melbourne-Bielefeld Seminar on Random Matrix Theory (2019 - 2021)

KU Leuven

• Course on Approximation Theory

• Course on Complex Analysis

University of Trier

I was Teaching Assistant for several courses and lectures including

• Measure and Integration Theory (Maß- und Integrationstheorie)

• Analysis in One and Several Variables (Analysis in einer und mehreren Veränderlichen)

• Introduction to Number Theory and Algebra (Einführung in die Zahlentheorie und Algebra)

• Ordinary Differential Equations (Gewöhnliche Differentialgleichungen)

• Special Functions (Spezielle Funktionen) 

Selected Talks 

• Boundary Asymptotics of Non-Intersecting Brownian Motions: Pearcey, Airy and a Transition, Asymptotics, Randomness, Nonlinearity, Orthogonality, KU Leuven, May 2024

• Critical behavior of non-intersecting Brownian motions, KTH Royal Institute of Technology, Stockholm, October 2019

• Critical behavior for Gaussian perturbations of Hermitian matrices, Conference on Sums and Products of Random Matrices, ZiF Bielefeld, August 2018

• (Breakdown of) sine kernel universality for Dyson’s Brownian motion with deterministic initial conditions, Conference on Orthogonal Polynomials, Special Functions and Applications14, University of Kent, Canterbury UK, Juli 2017

• Asymptotic Zero Distribution of Jacobi-Piñeiro and Multiple Laguerre Polynomials, Invited Speaker at the Workshop for Special Functions and their Applications 2016, Copenhagen University, Denmark, November 2016.

• Moments and Spectral Densities of Singular Value Distributions for Products of Gaussian and Truncated Unitary Random Matrices, Invited Speaker at the Workshop on Random Matrices EurAsia 2016, University of Macau, China, July 2016.

• Jacobi Polynomial Moments and Products of Random Matrices, Conference on Orthogonal Polynomials, Special Functions and Applications 13, Gaithersburg, USA, June 2015.

• Plancherel-Rotach Formulas and Zero Asymptotics for Characteristic Polynomials of Random Matrices, Conference on Constructive Functions 2014, Vanderbilt University, Nashville, USA, May 2014.

• A Conjecture on Sparse Binomial-type Polynomials, Orthoquad Conference 2014, Tenerife, Spain, January 2014.