Stochastic Resetting Walk
stochastic-process · 37 views
stochastic-processstochastic
What It Is
Evans-Majumdar process: x(t+1) = x(t) + drift + Gauss noise, with Poisson-rate full reset to zero. Canonical model in non-equilibrium statistical physics for accumulation-with-catastrophe dynamics. Tests whether Forest Fire phenotype (ramp + reset) is detected without spatial-lattice coupling
Interpretation
Standard analysis sees: long-range memory (persistent); time-irreversible (slow rise, sharp collapse); nonstationary / drifting. The atlas finds no named structure, but the source is distinctively extreme on Navier-Stokes:cascade_asymmetry (-4.2z) — beyond what the standard bank predicts for it. It sits beside Levy Flight in the atlas (standard-bank rank 54) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.66
asymmetry0.83
occupancy0.66
short-range corr0.81
long-range memory0.95
spectral colour0.27
periodicity0.69
complexity0.63
time-irreversibility0.00
volatility clustering0.84
multifractality0.77
dimensionality0.15
nonstationarity0.89
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Navier-Stokes:cascade_asymmetry | -4.2z | bank-miss 1.4σ |
Multifractal Spectrum:spectrum_width | +3.9z | bank-miss 1.0σ |
Higher-Order Statistics:kurt_max | +3.9z | bank-miss 1.1σ |
Wasserstein:transport_variability | +3.3z | bank-miss 1.1σ |
Time Reversibility:increment_skewness_max | +2.3z | bank-miss 1.1σ |
Composition
dtypefloat64
range[-0.03568, 1.841]
unique values16350 / 16384
mean ± std0.398 ± 0.361
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/Stochastic_Resetting_Walk.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Stochastic_Resetting_Walk.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Stochastic_Resetting_Walk.png)
Inflation (Substitution) > barcode
/d_curve/Stochastic_Resetting_Walk.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/Stochastic_Resetting_Walk.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/Stochastic_Resetting_Walk.png)
Ulam Spiral (Sacks) > default
/default/Stochastic_Resetting_Walk.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| BTC Close Price | 3.43 | cross-origin |
| Levy Flight | 3.92 | |
| ETH/BTC Ratio | 4.00 | cross-origin |
Which Geometries Light Up
Catch24 › Catch24:SC_FluctAnal_2_rsrangefit_50_1_logi_prop_r1 | rank 5/307 | 0.7660 |
Higher-Order Statistics › Higher-Order Statistics:kurt_max | rank 2/307 | 7.5289 |
Julia Set › Julia Set:potential_smoothness | rank 306/307 | 16.8373 |
Julia Set › Julia Set:potential_variance | rank 306/307 | 431.1089 |
Multifractal Spectrum › Multifractal Spectrum:spectrum_width | rank 3/307 | 0.5259 |
Navier-Stokes › Navier-Stokes:cascade_asymmetry | rank 307/307 | -1.0000 |
Septagonal (Danzer) › Septagonal (Danzer):z_conjugate | rank 305/307 | -0.6529 |
Symplectic › Symplectic:windowed_area_cv | rank 5/307 | 6.6042 |
Time Reversibility › Time Reversibility:increment_skewness_max | rank 2/307 | 1.0000 |
Ulam Spiral (Square) › Ulam Spiral (Square):radon_anisotropy | rank 5/307 | 0.0383 |
Wasserstein › Wasserstein:transport_variability | rank 3/307 | 0.1360 |
Wavelet Cascade › Wavelet Cascade:coarse_scale_kurtosis_slope | rank 307/307 | -2.8137 |
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