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Publications & Preprints

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Project C2: Fluctations and universality of random matrix esembles


Global Asymptotics for the Christoffel-Darboux Kernel of Random Matrix Theory
T. Kriecherbauer, K. Schubert, K. Schüler, M. Venker
Markov Process. Related Fields 21, no. 3, 639-694, 2015


Universality of General β -Ensembles
P. Bourgade, L. Erdös, H.-T. Yau
Duke Math. J. 163, no. 6 (2014), 1127-1190
Edge Universality of Beta Ensembles
P. Bourgade, L. Erdös, H.-T. Yau
Comm. Math. Phys. 332 (2014) 261-354


Moderate deviations for the determinant of Wigner matrices
H. Doering, P. Eichelsbacher
Limit Theorems in Probability, Statistics and Number Theory, Springer Proceedings in Mathmatics & Statistics, 42 (2013) 253-276
The Local Semicircle Law for a General Class of Random Matrices
L. Erdös, A. Knowles, H.-T. Yau, J. Yin
Electron. J. Probab. 18 (2013) 1-58
Spectral statistics of Erdös-Rényi graphs I: Local semicircle law
L. Erdös, A. Knowles, H.-T. Yau, J. Yin
Annals of Probability 2013, Vol. 41, No. 3B, 2279-2375
Moderate deviations via cumulants
H. Doering, P. Eichelsbacher
Journal of Theoretical Probab. 26 (2013) 360-385
Die Lindeberg Methode in der Theorie der Zufallsmatrizen
F. Gerle

Master thesis, Ruhr-Universität Bochum (2013)


Zeros and ratio asymptotics for matrix orthogonal polynomials
S. Delvaux, H. Dette
J. Anal. Math. 118 (2012), 657-690
Distributions on matrix moment spaces
H. Dette, M. Guhlich, J. Nagel
Edge fluctuations of eigenvalues of Wigner matrices
H. Döring, P. Eichelsbacher
Distributions on unbounded moment spaces and random moment sequences
H. Dette und J. Nagel
Ann. Probab. Volume 40, Number 6 (2012), 2690-2704
Spectral Statistics of Erdös-Rényi Graphs II: Eigenvalue Spacing and the Extreme Eigenvalues
L. Erdös, A. Knowles, H.-T. Yau, J. Yin
Comm. Math. Phys. 314 (2012) 587-640
Wigner theorems with correlations and deviations for the largest eigenvalue of biorthogonal ensembles
K. Credner

PhD thesis, Ruhr-Universität Bochum (06/2012)
New developments in Stein's method with applications
Ch. Döbler

PhD thesis, Ruhr-Universität Bochum (11/2012)
Ein zentraler Grenzwertsatz für die Anzahl der Eigenwerte von Wignermatrizen
F. König

Master thesis, Ruhr-Universität Bochum (2012)
On the convergence of the nearest neighbour eigenvalue spacing distribution for the orthogonal and symplectic ensembles
K. Schubert

PhD thesis, Ruhr-Universität Bochum (04/2012)
Untersuchungen der Konvergenzraten für matrixwertige Riemann-Hillbert Probleme im Fall endlicher Regularität
A. Werner

PhD thesis, Ruhr-Universität Bochum (10/2012)


Large deviations for disordered bosons and multiple orthogonal polynomial ensembles
P. Eichelsbacher, J. Sommerauer, M. Stolz
abstract math-ph/1102.0792
J. Math. Phys. 52, 073510, (2011).
Moderate deviations for the eigenvalue counting function of Wigner matrices
H. Doering, P. Eichelsbacher
Latin American Journal of Probability and Mathematical Statistics 2013
Universality of Random Matrices and Local Relaxation Flow
L. Erdös, B. Schlein, H.-T. Yau
Invent. Math. 185 (2011) 75-119


Random block matrices and matrix orthogonal polynomials
H. Dette, B. Reuther
abstract math/0809.4601
Theor. Probab. 23 (2010), 378-400
Stein's method for dependent random variables occurring in Statistical Mechanics
P. Eichelsbacher, M. Löwe
abstract math/0908.1909
Electronic J. Probab. 15 (2010), no.30, 962-988
Fluctuations of eigenvalues of matrix models and their applications
T. Kriecherbauer, M. Shcherbina
abstract math-ph/1003.6121
Process level moderate deviations for stabilizing functionals
P. Eichelsbacher, T. Schreiber
abstract math/0603402
ESAIM Probab. Stat. 14 (2010), 1-15
A pedestrian's view on interacting particle systems, KPZ universality, and random matrices
T. Kriecherbauer, J. Krug
abstract cond-mat/0803.2796
J. Phys. A: Math. Theor. 43 (2010), 403001, 52 pp
Universality of sine-kernel for Wigner matrices with a small Gaussian perturbation
L. Erdoes, J. Ramirez, B. Schlein, H.-T. Yau
abstract math-ph/0905.2089
Electr. J. Prob. 15, Paper 18, 526-604 (2010)
Bulk Universality for Wigner Matrices
L. Erdoes, S. Peche, J. Ramirez, B. Schlein, H.-T. Yau
abstract math-ph/0905.4176
Comm. Pure Appl. Math. 63, No. 7, 895-925 (2010)
Bulk Universality for Wigner Hermitian matrices with subexponential decay
L. Erdoes, J. Ramirez, B. Schlein, T. Tao, V. Vu, H.-T. Yau
abstract math/0906.4400
Math. Res. Lett. 17 (2010), no. 4, 667-674
Universality of Wigner Random Matrices
L. Erdoes
abstract math-ph/0909.2691
Proceedings of the XVI-th ICMP, Prague, World Scientific, 99-105 (2010)
Random block matrices generalizing the classical Jacobi and Laguerre ensembles
H. Dette, M. Guhlich, J. Nagel

Jour. of Multiv. Analysis, 101 (2010), 1884-1897
Distributions on unbounded moment spaces and random moment sequences
H. Dette, J. Nagel
abstract math/1007.3369
Universality of Random Matrices and Local Relaxation Flow
L. Erdoes, B. Schlein, H.-T. Yau
abstract math-ph/0907.5605
The local relaxation flow approach to universality of the local statistics for random matrices
L. Erdoes, B. Schlein, H.-T. Yau, J. Yin
abstract math-ph/0911.3687
Accepted to Annales Inst. H. Poincaré (B), Probability and Statistics
Universality for generalized Wigner matrices with Bernoulli distribution
L. Erdoes, H.-T. Yau, J. Yin
abstract math-ph/1003.3813
Universality of Wigner Random Matrices: a Survey of Recent Results
L. Erdoes
abstract math-ph/1004.0861
Rigidity of Eigenvalues of Generalized Wigner Matrices
L. Erdoes, H.-T. Yau, J. Yin
abstract math-ph/1007.4652
On rates of convergence in the Curie-Weiss-Potts model with external field
P. Eichelsbacher, B. Martschink
abstract math/1011.0319
Large Deviations for Random Matricial Moment Problems
Jan Nagel, Jens Wagener, Fabrice Gamboa, Alain Rouault
abstract math/1011.0299
Stein's method and the multivariate CLT for traces of powers on the classical compact groups
Christian Doebler, Michael Stolz
abstract math.PR/1012.3730
Moderate deviations via cumulants
Hanna Döring, Peter Eichelsbacher
abstract math.PR/1012.5027


Some asymptotic properties of the spectrum of the Jacobi ensemble
H. Dette, J. Nagel
abstract math/0904.4091
SIAM Journal on Math. Ana. 41 (2009), 1491-1507
Moderate deviations in random graphs and Bernoulli random matrices
H. Döring, P. Eichelsbacher
abstract math/0901.3246
Journal-ref: Electronic Journal of Probability, Vol. 14, 2009, Paper no. 92, 2636-2656
A note on random orthogonal polynomials on a compact interval
M. Birke, H. Dette
abstract math/0809.4936
Proc. Amer. Math. Soc. 137 (2009), no. 10, 3511-3522
Matrix measures, random moments and Gaussian ensembles
J. Nagel, H. Dette
abstract math/0904.3847
Fluctuations for traces of words in a multi-matrix model
P. Eichelsbacher, J. Sommerauer

Electron. Commun. Probab. 14 (2009), 572-586


Borel theorems for random matrices from the classical compact symmetric spaces
B. Collins, M. Stolz
abstract math/0611708
Annals of Probability 2008, Vol. 36, No. 3, 876-895
Moderate deviations for some point measures in geometric probability
Yu Baryshnikov, P. Eichelsbacher, T. Schreiber, J. E. Yukich
abstract math/0603022
Annales de l'Institut Henri Poincaré - Probabilités et Statistiques 2008, Vol. 44, No. 3, 422-446
Ordered random walks
P. Eichelsbacher, W. Koenig
abstract math/0610850
Electronic J. Probab. 13 (2008), no. 46, 1307-1336
Stein's method for discrete Gibbs measures
P. Eichelsbacher, G. Reinert
abstract math/0808.2877
Annals of Applied Probability 2008, Vol. 18, No. 4, 1588-1618
Large deviations for random matrix ensembles in mesoscopic physics
P. Eichelsbacher, M. Stolz
abstract math/0610811
Markov Process. Related Fields 14 (2008), no. 2, 207-232
Wigner theorems for random matrices with dependent entries: Ensembles associated to symmetric spaces and sample covariance matrices
K. Hofmann-Credner, M. Stolz
abstract math/0707.2333
Elect. Comm. in Probab. 13 (2008), 401--414


Universality for orthogonal and symplectic Laguerre-type ensembles
P. Deift, D. Gioev, T. Kriecherbauer, M. Vanlessen
abstract math-ph/0612007
J. Stat. Phys. 129 (2007), no. 5-6, 949-1053


Asymptotics of matrix integrals and tensor invariants of compact Lie groups
M. Stolz, T. Tate
abstract math.RT/0610720
Proc. Amer. Math. Soc. 136 (2008), 2235-2244
Lifschitz tails and localisation for a class of Schroedinger operators with random breather-type potential
W. Kirsch, I. Veselic'
abstract math-ph/0609014


Bessel convolutions on matrix cones
M. Rösler
abstract math.CA/0512474
Compos. Math. 143 (2007), no. 3, 749-779
Strong asymptotics of Laguerre-type orthogonal polynomials and applications in random matrix theory
M. Vanlessen
abstract math.CA/0504604
Constr. Approx. 25 (2007), no. 2, 125-175
On the Diaconis-Shahshahani Method in Random Matrix Theory
M. Stolz
J. Algebraic Combin. 22 (2005), 471-491
Fluctuation in a p-spin interaction model
H. Knöpfel, M. Löwe

Ann. Inst. H. Poincare Probab. Statist Vol. 41 (2005), no. 4, 807-815.
Lifshits tails for spectra of Erdoes-Renyi random graphs
O. Khorunzhiy, W. Kirsch, P. Müller
abstract math-ph/0502054
Annals of Applied Probability 2006, Vol. 16, No. 1, 295-309


Lifshits tails caused by anisotropic decay: the emergence of a quantum-classical regime
W. Kirsch, S. Warzel
abstract math-ph/0412079
Spectral properties of the Laplacian on bond-percolation graphs
W. Kirsch, P. Müller
abstract math-ph/0407047
Math. Z. 252 (2006) 899 - 916
The band-edge behavior of the density of surfacic states
W. Kirsch, F. Klopp
abstract math-ph/0407051
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