Student-t Noise
stochastic-process · 37 views
stochastic-processstochastic
What It Is
IID Student-t noise, df=3 --- symmetric heavy tails (finite variance, infinite kurtosis), a milder-tailed companion to Stable Noise. Antithetic-symmetrized so in-sample skew, mean, and time-irreversibility are exactly zero. The second heavy-tail contrast control: agreement between two distinct tail laws keeps a downstream verdict from hinging on one mechanism.
Interpretation
Standard analysis sees: heavy-tailed; aperiodic / broadband; high-complexity (noise-like). The atlas finds no named structure, but the source is distinctively extreme on SL(2,ℝ) (Thurston):parabolic_fraction (+5.8z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.93
asymmetry0.41
occupancy0.28
short-range corr0.34
long-range memory0.41
spectral colour0.72
periodicity0.06
complexity0.94
time-irreversibility0.63
volatility clustering0.29
multifractality0.46
dimensionality0.72
nonstationarity0.55
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
SL(2,ℝ) (Thurston):parabolic_fraction | +5.8z | bank-miss 1.2σ |
Fisher Information:geodesic_velocity | +3.1z | bank-miss 2.1σ |
Fractal (Mandelbrot):interior_fraction | +2.4z | bank-miss 1.7σ |
Composition
dtypefloat64
range[-43.53, 43.53]
unique values16384 / 16384
mean ± std-1.73e-18 ± 1.72
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/Student-t_Noise.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Student-t_Noise.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Student-t_Noise.png)
Inflation (Substitution) > barcode
/d_curve/Student-t_Noise.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/Student-t_Noise.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/Student-t_Noise.png)
Ulam Spiral (Sacks) > default
/default/Student-t_Noise.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Stable Noise | 2.24 | |
| BTC Returns | 2.57 | cross-origin |
| Nikkei Returns | 3.23 | cross-origin |
Which Geometries Light Up
Fisher Information › Fisher Information:geodesic_velocity | rank 3/306 | 1.6483 |
Fractal (Mandelbrot) › Fractal (Mandelbrot):interior_fraction | rank 2/306 | 0.9937 |
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):mean_hyperbolic_radius | rank 305/306 | 0.1087 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):parabolic_fraction | rank 2/306 | 0.7484 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):cocycle_growth_burstiness | rank 302/306 | 0.0090 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):cocycle_growth_rate | rank 304/306 | 0.0147 |
Sol (Thurston) › Sol (Thurston):path_length | rank 303/306 | 8609.0549 |
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