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Publications & Preprints

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Project C2: Fluctations and universality of random matrix esembles

2015

Global Asymptotics for the Christoffel-Darboux Kernel of Random Matrix Theory
T. Kriecherbauer, K. Schubert, K. Schüler, M. Venker
arXiv:1401.6772
Markov Process. Related Fields 21, no. 3, 639-694, 2015

2014

Universality of General β -Ensembles
P. Bourgade, L. Erdös, H.-T. Yau
arXiv:1104.2272
Duke Math. J. 163, no. 6 (2014), 1127-1190
Edge Universality of Beta Ensembles
P. Bourgade, L. Erdös, H.-T. Yau
arXiv:1306.5728
Comm. Math. Phys. 332 (2014) 261-354

2013

Moderate deviations for the determinant of Wigner matrices
H. Doering, P. Eichelsbacher
arXiv:1301.2915
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
arXiv:1212.0164
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
arXiv:1103.1919
Annals of Probability 2013, Vol. 41, No. 3B, 2279-2375
Moderate deviations via cumulants
H. Doering, P. Eichelsbacher
arXiv:1012.5027
Journal of Theoretical Probab. 26 (2013) 360-385
Die Lindeberg Methode in der Theorie der Zufallsmatrizen
F. Gerle

Master thesis, Ruhr-Universität Bochum (2013)

2012

Zeros and ratio asymptotics for matrix orthogonal polynomials
S. Delvaux, H. Dette
arXiv:1108.5155
J. Anal. Math. 118 (2012), 657-690
Distributions on matrix moment spaces
H. Dette, M. Guhlich, J. Nagel
preprint
Edge fluctuations of eigenvalues of Wigner matrices
H. Döring, P. Eichelsbacher
arXiv:1203.2115
Distributions on unbounded moment spaces and random moment sequences
H. Dette und J. Nagel
abstract
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
arXiv:1103.3869
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)

2011

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
arXiv:1104.0221
Latin American Journal of Probability and Mathematical Statistics 2013
Universality of Random Matrices and Local Relaxation Flow
L. Erdös, B. Schlein, H.-T. Yau
arXiv:0907.5605
Invent. Math. 185 (2011) 75-119

2010

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

2009

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

2008

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

2007

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

2006

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

2005

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
PDF
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

2004

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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