51 citations · 251 across the 19 of their papers we have counts for
12 papers · 1 filter
Glass--like transition described by toppling of stability hierarchy
Jacek Grela, Boris A. Khoruzhenko
Building on the work of Fyodorov (2004) and Fyodorov and Nadal (2012) we examine the critical behaviour of population of saddles with fixed instability index in high dimensiona…
Eikonal formulation of large dynamical random matrix models
Jacek Grela, Maciej A. Nowak, Wojciech Tarnowski
Standard approach to dynamical random matrix models relies on the description of trajectories of eigenvalues. Using the analogy from optics, based on the duality between the Fermat…
Full Dysonian dynamics of the complex Ginibre ensemble
Jacek Grela, Piotr Warchoł
We find stochastic equations governing eigenvalues and eigenvectors of a dynamical complex Ginibre ensemble reaffirming the intertwined role played between both sets of matrix degr…
On characteristic polynomials for a generalized chiral random matrix ensemble with a source
Yan V Fyodorov, Jacek Grela, Eugene Strahov
We evaluate averages involving characteristic polynomials, inverse characteristic polynomials and ratios of characteristic polynomials for a random matrix taken from a…
Extreme matrices or how an exponential map links classical and free extreme laws
Jacek Grela, Maciej A. Nowak
Using the proposed by us thinning approach to describe extreme matrices, we find an explicit exponentiation formula linking classical extreme laws of Fréchet, Gumbel and Weibull gi…
Exact spectral densities of complex noise-plus-structure random matrices
Jacek Grela, Thomas Guhr
We use supersymmetry to calculate exact spectral densities for a class of complex random matrix models having the form , where is a random noise part and a…
Ornstein-Uhlenbeck diffusion of hermitian and non-hermitian matrices - unexpected links
Jean-Paul Blaizot, Jacek Grela, Maciej A. Nowak +2
We compare the Ornstein-Uhlenbeck process for the Gaussian Unitary Ensemble to its non-hermitian counterpart - for the complex Ginibre ensemble. We exploit the mathematical framewo…
Hydrodynamical spectral evolution for random matrices
P. J. Forrester, J. Grela
The eigenvalues of the matrix structure , where is a random Gaussian Hermitian matrix and is non-random or random independent of , are closely related…
Diffusion method in Random Matrix Theory
Jacek Grela
We introduce a simple yet powerful calculational tool useful in calculating averages of ratios and products of characteristic polynomials. The method is based on Dyson Brownian mot…
Unveiling the significance of eigenvectors in diffusing non-hermitian matrices by identifying the underlying Burgers dynamics
Zdzislaw Burda, Jacek Grela, Maciej A. Nowak +2
Following our recent letter, we study in detail an entry-wise diffusion of non-hermitian complex matrices. We obtain an exact partial differential equation (valid for any matrix si…
Diffusion in the space of complex Hermitian matrices - microscopic properties of the averaged characteristic polynomial and the averaged inverse characteristic polynomial
Jean-Paul Blaizot, Jacek Grela, Maciej A. Nowak +1
We show that the averaged characteristic polynomial and the averaged inverse characteristic polynomial, associated with Hermitian matrices whose elements perform a random walk in t…
Dysonian dynamics of the Ginibre ensemble
Zdzisław Burda, Jacek Grela, Maciej A. Nowak +2
We study the time evolution of Ginibre matrices whose elements undergo Brownian motion. The non-Hermitian character of the Ginibre ensemble binds the dynamics of eigenvalues to the…