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Wigner's Semicircle Law
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Summary
Wigner's Semicircle Law
describes the
Distribution of eigenvalues
of
Large random symmetric matrices
, stating that as the
Matrix size
increases, the
Density of eigenvalues
approaches a
Semicircular Distribution
. This law is foundational in
Random Matrix Theory
and has
Applications In Physics
, particularly in understanding
Energy levels in heavy nuclei
and
Quantum Chaos
.
Concepts
Random Matrix Theory
Eigenvalue Distribution
Symmetric Matrices
Quantum Chaos
Spectral Density
Nuclear Physics
Large Matrix Limit
Semicircular Distribution
Semicircle Distribution
Random Matrices
Gaussian Unitary Ensemble
Relevant Degrees
Algebra 63%
Probability and Statistics 38%
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