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Nonlinear Analogue of the May-Wigner Instability Transition
(PNAS, 2016-01)
We study a system of $N\gg 1$ degrees of freedom coupled via a smooth homogeneous Gaussian vector field with both gradient and divergence-free components. In the absence of coupling, the system is exponentially relaxing ...
Resonance width distribution in RMT: Weak coupling regime beyond Porter-Thomas
We employ the random matrix theory (RMT) framework to revisit the distribution of resonance widths in quantum chaotic systems weakly coupled to the continuum via a finite number M of open channels. In contrast to the ...
On the distribution of maximum value of the characteristic polynomial of GUE random matrices
Motivated by recently discovered relations between logarithmically correlated Gaussian processes and characteristic polynomials of large random $N \times N$ matrices $H$ from the Gaussian Unitary Ensemble (GUE), we consider ...
Counting equilibria of large complex systems by instability index
We consider a nonlinear autonomous system of $N\gg 1$ degrees of freedom randomly coupled by both relaxational ('gradient') and non-relaxational ('solenoidal') random interactions. We show that with increased interaction ...