# Random matrix theory and applications assignment help

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The exhaustive list of topics in Random Matrix Theory and Applications in which we provide Help with Homework Assignment and Help with Project is as follows:

• Maximum entropy approach of complex systems:
• Probability and information entropy: the role of the relevant physical parameters as constraints.
• The role of symmetries in motivating a natural probability measure e.g Gaussian or uniform etc.
• The maximum entropy criterion in the context of statistical inferences.
• Random matrix ensembles:
• Nature of ensemble: Role of symmetry, interactions and other system conditions.
• Basis invariance vs Basis dependence of the ensemble and their transformation properties.
• Stationary vs non-stationary ensembles.
• Conservative systems and Gaussian ensembles of Hermitian matrices: ten standard types.
• Non-conservative systems and ensembles of non-Hermitian matrices: Ginibre ensembles.
• Time-periodic systems and circular ensembles of unitary matrices.
• Laguerre ensembles.
• Multi-cut ensembles.
• Correlations and fluctuation measures:
• Fluctuation measures of eigenvalues e.g. number variance, spacing distribution, spectral rigidity, gap probabilities etc.
• Fluctuations measures of eigenfunctions e.g local intensity distribution, inverse participation ratio, local density of states etc.
• Level density and level repulsion: role of global symmetries.
• Eigenfunction localization: role of interactions and disorder.
• Behavior at the edge of the spectrum.
• Critical level statistics and multifractality of eiegnfunctions.
• Universality of fluctuations measures.
• System dependent random matrix ensembles:
• Varying system conditions and transition between stationary ensembles.
• Common mathematical formulation of fluctuation measures for multi-parametric Gaussian ensembles.
• Connection to one and two dimensional Calogero-Sutherland Hamiltonian of interacting particles.
• Phase transition and critical ensembles.
• Correlated random matrix ensembles.
• Random matrices to quantum systems:
• Random matrix theory of quantum transport.
• Random matrix theory of quantum chaotic systems.
• Disordered systems.
• Quantum gravity.
• Nuclear resonances, Atoms, molecules etc..
• Random matrices to classical systems:
• Financial systems e.g stock market fluctuations.
• Biological systems e.g signals received by brain.
• Atmospheric correlations.
• Complex networks e.g traffic systems.
• Light propagation through random media.
• Elastomechanics.
• Number theoretic systems e.g. Reimann-zeta function.