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Eigenvalue Repulsion
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Summary
Eigenvalue Repulsion
is a phenomenon observed in
Random Matrix Theory
where
Eigenvalues of large random matrices
tend to avoid each other, leading to a
Spacing distribution
that differs from that of
Uncorrelated random variables
. This behavior is crucial in understanding
Complex Systems
such as
Quantum Chaos
, where it reflects the
Underlying correlations
and
Interactions within the system
.
Concepts
Random Matrix Theory
Quantum Chaos
Eigenvalue Distribution
Level Spacing Statistics
Wigner-Dyson Distribution
Universality Classes
Spectral Correlations
Hermitian Matrices
GOE, GUE, GSE Ensembles
Symmetry Classes
Eigenvalue Statistics
Relevant Degrees
Algebra 100%
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