The Experts below are selected from a list of 17871 Experts worldwide ranked by ideXlab platform
Yan V Fyodorov - One of the best experts on this subject based on the ideXlab platform.
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on statistics of bi orthogonal eigenvectors in Real and complex ginibre ensembles combining partial schur decomposition with supersymmetry
Communications in Mathematical Physics, 2018Co-Authors: Yan V FyodorovAbstract:We suggest a method of studying the joint probability density (JPD) of an Eigenvalue and the associated ‘non-orthogonality overlap factor’ (also known as the ‘Eigenvalue condition number’) of the left and right eigenvectors for non-selfadjoint Gaussian random matrices of size $${N\times N}$$ . First we derive the general finite N expression for the JPD of a Real Eigenvalue $${\lambda}$$ and the associated non-orthogonality factor in the Real Ginibre ensemble, and then analyze its ‘bulk’ and ‘edge’ scaling limits. The ensuing distribution is maximally heavy-tailed, so that all integer moments beyond normalization are divergent. A similar calculation for a complex Eigenvalue z and the associated non-orthogonality factor in the complex Ginibre ensemble is presented as well and yields a distribution with the finite first moment. Its ‘bulk’ scaling limit yields a distribution whose first moment reproduces the well-known result of Chalker and Mehlig (Phys Rev Lett 81(16):3367–3370, 1998), and we provide the ‘edge’ scaling distribution for this case as well. Our method involves evaluating the ensemble average of products and ratios of integer and half-integer powers of characteristic polynomials for Ginibre matrices, which we perform in the framework of a supersymmetry approach. Our paper complements recent studies by Bourgade and Dubach (The distribution of overlaps between eigenvectors of Ginibre matrices, 2018. arXiv:1801.01219 ).
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on statistics of bi orthogonal eigenvectors in Real and complex ginibre ensembles combining partial schur decomposition with supersymmetry
arXiv: Mathematical Physics, 2017Co-Authors: Yan V FyodorovAbstract:We suggest a method of studying the joint probability density (JPD) of an Eigenvalue and the associated 'non-orthogonality overlap factor' (also known as the 'Eigenvalue condition number') of the left and right eigenvectors for non-selfadjoint Gaussian random matrices of size $N\times N$. First we derive the general finite $N$ expression for the JPD of a Real Eigenvalue $\lambda$ and the associated non-orthogonality factor in the Real Ginibre ensemble, and then analyze its 'bulk' and 'edge' scaling limits. The ensuing distribution is maximally heavy-tailed, so that all integer moments beyond normalization are divergent. A similar calculation for a complex Eigenvalue $z$ and the associated non-orthogonality factor in the complex Ginibre ensemble is presented as well and yields a distribution with the finite first moment. Its 'bulk' scaling limit yields a distribution whose first moment reproduces the well-known result of Chalker and Mehlig \cite{ChalkerMehlig1998}, and we provide the 'edge' scaling distribution for this case as well. Our method involves evaluating the ensemble average of products and ratios of integer and half-integer powers of characteristic polynomials for Ginibre matrices, which we perform in the framework of a supersymmetry approach. Our paper complements recent studies by Bourgade and Dubach \cite{BourgadeDubach}.
Oleg Zaboronski - One of the best experts on this subject based on the ideXlab platform.
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on the distribution of the largest Real Eigenvalue for the Real ginibre ensemble
Annals of Applied Probability, 2017Co-Authors: Mihail Poplavskyi, Roger Tribe, Oleg ZaboronskiAbstract:Let N−−√+λmaxN+λmax be the largest Real Eigenvalue of a random N×NN×N matrix with independent N(0,1)N(0,1) entries (the “Real Ginibre matrix”). We study the large deviations behaviour of the limiting N→∞N→∞ distribution P[λmax 0t>0, P[λmax
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on the distribution of the largest Real Eigenvalue for the Real ginibre ensemble
arXiv: Probability, 2016Co-Authors: Mihail Poplavskyi, Roger Tribe, Oleg ZaboronskiAbstract:Let $\sqrt{N}+\lambda_{max}$ be the largest Real Eigenvalue of a random $N\times N$ matrix with independent $N(0,1)$ entries (the `Real Ginibre matrix'). We study the large deviations behaviour of the limiting $N\rightarrow \infty$ distribution $P[\lambda_{max} 0$, \[ P[\lambda_{max}
Mihail Poplavskyi - One of the best experts on this subject based on the ideXlab platform.
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on the distribution of the largest Real Eigenvalue for the Real ginibre ensemble
Annals of Applied Probability, 2017Co-Authors: Mihail Poplavskyi, Roger Tribe, Oleg ZaboronskiAbstract:Let N−−√+λmaxN+λmax be the largest Real Eigenvalue of a random N×NN×N matrix with independent N(0,1)N(0,1) entries (the “Real Ginibre matrix”). We study the large deviations behaviour of the limiting N→∞N→∞ distribution P[λmax 0t>0, P[λmax
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on the distribution of the largest Real Eigenvalue for the Real ginibre ensemble
arXiv: Probability, 2016Co-Authors: Mihail Poplavskyi, Roger Tribe, Oleg ZaboronskiAbstract:Let $\sqrt{N}+\lambda_{max}$ be the largest Real Eigenvalue of a random $N\times N$ matrix with independent $N(0,1)$ entries (the `Real Ginibre matrix'). We study the large deviations behaviour of the limiting $N\rightarrow \infty$ distribution $P[\lambda_{max} 0$, \[ P[\lambda_{max}
E Camposcanton - One of the best experts on this subject based on the ideXlab platform.
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widening of the basins of attraction of a multistable switching dynamical system with the location of symmetric equilibria
Nonlinear Analysis: Hybrid Systems, 2017Co-Authors: L J Ontanongarcia, E CamposcantonAbstract:Abstract A switching dynamical system by means of piecewise linear systems in R 3 that presents multistability is presented. The flow of the system displays multi-scroll attractors due to the unstable hyperbolic focus-saddle equilibria with stability index of type I, i.e., a negative Real Eigenvalue and a pair of complex conjugated Eigenvalues with positive Real part. This class of systems is constructed by a discrete control mode changing the equilibrium point regarding the location of their states. The scrolls appear when the stable and unstable eigenspaces of each adjacent equilibrium point generate the stretching and folding mechanisms needed in chaos, i.e., the unstable manifold in the first subsystem carries the trajectory towards the stable manifold of the immediate adjacent subsystem. The resulting attractors are located around four focus saddle equilibria. If the equilibria are located symmetrically to one of the axes and the distance between each equilibria is properly adjusted to generate two double-scroll chaotic attractors, the system can present from bistable to multistable parallel solutions regarding the position of their initial states. In addition the resulting basin of attraction presents a significatively widening when the distance between the equilibria of the parallel attractors is displaced.
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analog electronic implementation of a class of hybrid dissipative dynamical system
International Journal of Bifurcation and Chaos, 2016Co-Authors: L J Ontanongarcia, E Camposcanton, Ricardo FematAbstract:An analog electronic implementation by means of operational amplifiers of a class of hybrid dissipative systems in R3 is presented. The switching systems have two unstable hyperbolic focus-saddle equilibria with the same stability index, a positive Real Eigenvalue and a pair of complex conjugated Eigenvalues with negative Real part. The analog circuit generates signals that oscillate in an attractor located between the two unstable equilibria, and may present saturation states at the moment of energizing it, i.e. if the initial voltage on the capacitors do not belong to the basin of attraction the circuit will end on a saturation state.
Luca Zaccarian - One of the best experts on this subject based on the ideXlab platform.
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design of marx generators as a structured Eigenvalue assignment
Automatica, 2014Co-Authors: Sergio Galeani, Alain Jacquemard, Didier Henrion, Luca ZaccarianAbstract:We consider the design problem for a Marx generator electrical network, a pulsed power generator. We show that the components design can be conveniently cast as a structured Real Eigenvalue assignment with significantly lower dimension than the state size of the Marx circuit. Then we present two possible approaches to determine its solutions. A first symbolic approach consists in the use of Grobner basis representations, which allows us to compute all the (finitely many) solutions. A second approach is based on convexification of a nonconvex optimization problem with polynomial constraints. We also comment on the conjecture that for any number of stages the problem has finitely many solutions, which is a necessary assumption for the proposed methods to converge. We regard the proof of this conjecture as an interesting challenge of general interest in the Real algebraic geometry field.
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design of marx generators as a structured Eigenvalue assignment
arXiv: Optimization and Control, 2013Co-Authors: Sergio Galeani, Alain Jacquemard, Didier Henrion, Luca ZaccarianAbstract:We consider the design problem for a Marx generator electrical network, a pulsed power generator. The engineering specification of the design is that a suitable resonance condition is satisfied by the circuit so that the energy initially stored in a number of storage capacitors is transferred in finite time to a single load capacitor which can then store the total energy and deliver the pulse. We show that the components design can be conveniently cast as a structured Real Eigenvalue assignment with significantly lower dimension than the state size of the Marx circuit. Then we comment on the nontrivial nature of this structured Real Eigenvalue assignment problem and present two possible approaches to determine its solutions. A first symbolic approach consists in the use of Gr\"obner basis representations, which allows us to compute all the (finitely many) solutions. A second approach is based on convexification of a nonconvex optimization problem with polynomial constraints. We show that the symbolic method easily provides solutions for networks up to six stages while the numerical method can reach up to seven and eight stages. We also comment on the conjecture that for any number of stages the problem has finitely many solutions, which is a necessary assumption for the proposed methods to converge. We regard the proof of this conjecture as an interesting challenge of general interest in the Real algebraic geometry field.
