@article{1506,
abstract = {Consider the square random matrix An = (aij)n,n, where {aij:= a(n)ij , i, j = 1, . . . , n} is a collection of independent real random variables with means zero and variances one. Under the additional moment condition supn max1≤i,j ≤n Ea4ij <∞, we prove Girko's logarithmic law of det An in the sense that as n→∞ log | detAn| ? (1/2) log(n-1)! d/→√(1/2) log n N(0, 1).},
author = {Bao, Zhigang and Pan, Guangming and Zhou, Wang},
journal = {Bernoulli},
number = {3},
pages = {1600 -- 1628},
publisher = {Bernoulli Society for Mathematical Statistics and Probability},
title = {{The logarithmic law of random determinant}},
doi = {10.3150/14-BEJ615},
volume = {21},
year = {2015},
}
@article{1508,
abstract = {We consider generalized Wigner ensembles and general β-ensembles with analytic potentials for any β ≥ 1. The recent universality results in particular assert that the local averages of consecutive eigenvalue gaps in the bulk of the spectrum are universal in the sense that they coincide with those of the corresponding Gaussian β-ensembles. In this article, we show that local averaging is not necessary for this result, i.e. we prove that the single gap distributions in the bulk are universal. In fact, with an additional step, our result can be extended to any C4(ℝ) potential.},
author = {Erdös, László and Yau, Horng},
journal = {Journal of the European Mathematical Society},
number = {8},
pages = {1927 -- 2036},
publisher = {European Mathematical Society},
title = {{Gap universality of generalized Wigner and β ensembles}},
doi = {10.4171/JEMS/548},
volume = {17},
year = {2015},
}
@article{1585,
abstract = {In this paper, we consider the fluctuation of mutual information statistics of a multiple input multiple output channel communication systems without assuming that the entries of the channel matrix have zero pseudovariance. To this end, we also establish a central limit theorem of the linear spectral statistics for sample covariance matrices under general moment conditions by removing the restrictions imposed on the second moment and fourth moment on the matrix entries in Bai and Silverstein (2004).},
author = {Bao, Zhigang and Pan, Guangming and Zhou, Wang},
journal = {IEEE Transactions on Information Theory},
number = {6},
pages = {3413 -- 3426},
publisher = {IEEE},
title = {{Asymptotic mutual information statistics of MIMO channels and CLT of sample covariance matrices}},
doi = {10.1109/TIT.2015.2421894},
volume = {61},
year = {2015},
}
@article{1674,
abstract = {We consider N × N random matrices of the form H = W + V where W is a real symmetric Wigner matrix and V a random or deterministic, real, diagonal matrix whose entries are independent of W. We assume subexponential decay for the matrix entries of W and we choose V so that the eigenvalues of W and V are typically of the same order. For a large class of diagonal matrices V, we show that the rescaled distribution of the extremal eigenvalues is given by the Tracy-Widom distribution F1 in the limit of large N. Our proofs also apply to the complex Hermitian setting, i.e. when W is a complex Hermitian Wigner matrix.},
author = {Lee, Jioon and Schnelli, Kevin},
journal = {Reviews in Mathematical Physics},
number = {8},
publisher = {World Scientific Publishing},
title = {{Edge universality for deformed Wigner matrices}},
doi = {10.1142/S0129055X1550018X},
volume = {27},
year = {2015},
}
@article{1677,
abstract = {We consider real symmetric and complex Hermitian random matrices with the additional symmetry hxy = hN-y,N-x. The matrix elements are independent (up to the fourfold symmetry) and not necessarily identically distributed. This ensemble naturally arises as the Fourier transform of a Gaussian orthogonal ensemble. Italso occurs as the flip matrix model - an approximation of the two-dimensional Anderson model at small disorder. We show that the density of states converges to the Wigner semicircle law despite the new symmetry type. We also prove the local version of the semicircle law on the optimal scale.},
author = {Alt, Johannes},
journal = {Journal of Mathematical Physics},
number = {10},
publisher = {American Institute of Physics},
title = {{The local semicircle law for random matrices with a fourfold symmetry}},
doi = {10.1063/1.4932606},
volume = {56},
year = {2015},
}
@article{2699,
abstract = {We prove the universality of the β-ensembles with convex analytic potentials and for any β >
0, i.e. we show that the spacing distributions of log-gases at any inverse temperature β coincide with those of the Gaussian β-ensembles.},
author = {Erdös, László and Bourgade, Paul and Yau, Horng},
journal = {Duke Mathematical Journal},
number = {6},
pages = {1127 -- 1190},
publisher = {Duke University Press},
title = {{Universality of general β-ensembles}},
doi = {10.1215/00127094-2649752},
volume = {163},
year = {2014},
}
@article{1926,
abstract = {We consider cross products of finite graphs with a class of trees that have arbitrarily but finitely long line segments, such as the Fibonacci tree. Such cross products are called tree-strips. We prove that for small disorder random Schrödinger operators on such tree-strips have purely absolutely continuous spectrum in a certain set.},
author = {Sadel, Christian},
journal = {Mathematical Physics, Analysis and Geometry},
number = {3-4},
pages = {409 -- 440},
publisher = {Springer},
title = {{Absolutely continuous spectrum for random Schrödinger operators on the Fibonacci and similar Tree-strips}},
doi = {10.1007/s11040-014-9163-4},
volume = {17},
year = {2014},
}
@article{1937,
abstract = {We prove the edge universality of the beta ensembles for any β ≥ 1, provided that the limiting spectrum is supported on a single interval, and the external potential is C4 and regular. We also prove that the edge universality holds for generalized Wigner matrices for all symmetry classes. Moreover, our results allow us to extend bulk universality for beta ensembles from analytic potentials to potentials in class C4.},
author = {Bourgade, Paul and Erdös, László and Yau, Horngtzer},
journal = {Communications in Mathematical Physics},
number = {1},
pages = {261 -- 353},
publisher = {Springer},
title = {{Edge universality of beta ensembles}},
doi = {10.1007/s00220-014-2120-z},
volume = {332},
year = {2014},
}
@article{2019,
abstract = {We prove that the empirical density of states of quantum spin glasses on arbitrary graphs converges to a normal distribution as long as the maximal degree is negligible compared with the total number of edges. This extends the recent results of Keating et al. (2014) that were proved for graphs with bounded chromatic number and with symmetric coupling distribution. Furthermore, we generalise the result to arbitrary hypergraphs. We test the optimality of our condition on the maximal degree for p-uniform hypergraphs that correspond to p-spin glass Hamiltonians acting on n distinguishable spin- 1/2 particles. At the critical threshold p = n1/2 we find a sharp classical-quantum phase transition between the normal distribution and the Wigner semicircle law. The former is characteristic to classical systems with commuting variables, while the latter is a signature of noncommutative random matrix theory.},
author = {Erdös, László and Schröder, Dominik J},
journal = {Mathematical Physics, Analysis and Geometry},
number = {3-4},
pages = {441 -- 464},
publisher = {Springer},
title = {{Phase transition in the density of states of quantum spin glasses}},
doi = {10.1007/s11040-014-9164-3},
volume = {17},
year = {2014},
}
@article{2179,
abstract = {We extend the proof of the local semicircle law for generalized Wigner matrices given in MR3068390 to the case when the matrix of variances has an eigenvalue -1. In particular, this result provides a short proof of the optimal local Marchenko-Pastur law at the hard edge (i.e. around zero) for sample covariance matrices X*X, where the variances of the entries of X may vary.},
author = {Ajanki, Oskari H and Erdös, László and Krüger, Torben H},
journal = {Electronic Communications in Probability},
publisher = {Institute of Mathematical Statistics},
title = {{Local semicircle law with imprimitive variance matrix}},
doi = {10.1214/ECP.v19-3121},
volume = {19},
year = {2014},
}