78 citations · 542 across the 28 of their papers we have counts for
12 papers · 1 filter
On the asymptotic duality of spectral variances in random matrix theory and the "1/6" formula
Peng Tian, Roman Riser, Eugene Kanzieper
A "mysterious" relation between the number variance and the variance of the -th ordered eigenvalue, first suggested by French et al. [Ann. Phys. 113, 277 (1978)], is revisited a…
Statistics of local level spacings in single- and many-body quantum chaos
Peng Tian, Roman Riser, Eugene Kanzieper
We introduce a notion of local level spacings and study their statistics within a random-matrix-theory approach. In the limit of infinite-dimensional random matrices, we determine…
Power spectra and autocovariances of level spacings beyond the Dyson conjecture
Roman Riser, Peng Tian, Eugene Kanzieper
Introduced in the early days of random matrix theory, the autocovariances of level spacings accommodate a detailed information on correla…
Power spectrum of the circular unitary ensemble
Roman Riser, Eugene Kanzieper
We study the power spectrum of eigen-angles of random matrices drawn from the circular unitary ensemble and show that it can be evaluated in terms of either a Fredho…
Nonperturbative theory of power spectrum in complex systems
Roman Riser, Vladimir Al. Osipov, Eugene Kanzieper
The power spectrum analysis of spectral fluctuations in complex wave and quantum systems has emerged as a useful tool for studying their internal dynamics. In this paper, we formul…
Integrable Aspects of Universal Quantum Transport in Chaotic Cavities
Eugene Kanzieper
The Painlevé transcendents discovered at the turn of the XX century by pure mathematical reasoning, have later made their surprising appearance -- much in the way of Wigner's "mira…
Integrability of zero-dimensional replica field theories at beta=1
Pedro Vidal, Eugene Kanzieper
Building on insights from the theory of integrable lattices, the integrability is claimed for nonlinear replica sigma models derived in the context of real symmetric random matrice…
Non-Hermitean Wishart random matrices (I)
Eugene Kanzieper, Navinder Singh, Navinder Singh Bathinda
A non-Hermitean extension of paradigmatic Wishart random matrices is introduced to set up a theoretical framework for statistical analysis of (real, complex and real quaternion) st…
Correlations of RMT Characteristic Polynomials and Integrability: Hermitean Matrices
Vladimir Al. Osipov, Eugene Kanzieper
Integrable theory is formulated for correlation functions of characteristic polynomials associated with invariant non-Gaussian ensembles of Hermitean random matrices. By embedding…
A Note on the Pfaffian Integration Theorem
Alexei Borodin, Eugene Kanzieper
Two alternative, fairly compact proofs are presented of the Pfaffian integration theorem that is surfaced in the recent studies of spectral properties of Ginibre's Orthogonal Ensem…
Integrable Structure of Ginibre's Ensemble of Real Random Matrices and a Pfaffian Integration Theorem
Gernot Akemann, Eugene Kanzieper
In the recent publication [E. Kanzieper and G. Akemann, Phys. Rev. Lett. 95, 230201 (2005); arXiv: math-ph/0507058], an exact solution was reported for the probability "p_{n,k}" to…
Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices
Eugene Kanzieper, Gernot Akemann
The integrable structure of Ginibre's Orthogonal Ensemble of random matrices is looked at through the prism of the probability "p_{n,k}" to find exactly "k" real eigenvalues in the…