Wigner Semicircle
random-matrix-quantum · 37 views
random-matrix-quantumspectral-RMT
What It Is
Eigenvalue density from large random matrices --- converges to the Wigner semicircle law; for the emitted support [-1, 1] this is ρ(x)=(2/π)√(1-x²) (the √(4-x²)/(2π) form is the radius-2 convention)
Interpretation
Standard analysis sees: rich, high-entropy values; aperiodic / broadband; high-complexity (noise-like); monofractal; high-dimensional / space-filling. The atlas detects no named structure beyond this.
What standard analysis sees
tail heaviness0.36
asymmetry0.48
occupancy0.86
short-range corr0.29
long-range memory0.30
spectral colour0.67
periodicity0.00
complexity0.98
time-irreversibility0.35
volatility clustering0.19
multifractality0.10
dimensionality0.98
nonstationarity0.36
What the atlas adds
Nothing beyond the standard reading — this source’s structure is already captured by standard features; the atlas adds no named residual.
Composition
dtypefloat64
range[-1.054, 1.038]
unique values16384 / 16384
mean ± std-0.000581 ± 0.502
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > free_plate_nodal
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Wigner_Semicircle.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Wigner_Semicircle.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Wigner_Semicircle.png)
Inflation (Substitution) > barcode
/d_curve/Wigner_Semicircle.png)
Inflation (Substitution) > d_curve
Information Theory > default
Julia Set > escape_histogram
Klein Bottle > default
Laplacian > default
Logarithmic Spiral > default
Möbius-S³ > mobius_cylinder
Möbius-S³ > s2_base_map
Ordinal Partition > default
/phi_spectrum/Wigner_Semicircle.png)
Penrose (Quasicrystal) > phi_spectrum
Persistent Homology > barcode
Persistent Homology > h1_diagram
Predictability > default
Recurrence Quantification > default
Spectral Analysis > default
Spectral Graph > default
Spirograph > mode_spectrum
Spirograph > phasor_trajectory
Symplectic > flux_grid
Symplectic > phase_space
/default/Wigner_Semicircle.png)
Ulam Spiral (Sacks) > default
/default/Wigner_Semicircle.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| ChaCha20 | 1.95 | cross-origin |
| AES Encrypted | 2.09 | cross-origin |
| BSL Residues | 2.11 | cross-origin |
Which Geometries Light Up
Möbius-S³ › Möbius-S³:phase_profile_deviation | rank 306/307 | 0.1087 |
Predictability › Predictability:sample_entropy | rank 3/307 | 2.2365 |
S² × ℝ (Thurston) › S² × ℝ (Thurston):bingham_concentration | rank 307/307 | 0.3922 |
← Spectral Form Factorin algorithmic-bytes
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