Sections / Section 13: Hierarchical Architecture / spectralGapRatio

Spectral Gap Ratio

defprovedHierarchy

Documentation

Lean 4 Proof

def spectralGapRatio (rSlow rFast : ℝ) : ℝ := rFast / rSlow

Dependency Graph

Used by

timescale_ratio_eq_rate_ratio large_gap_implies_separation

Location

thesis/CESProofs/Hierarchy/SpectralHierarchy.lean:50

Module Section

Endogenous Hierarchy: Why N Levels?

In the same file

adjustmentRate timescaleFromRate timescale_ratio_eq_rate_ratio large_gap_implies_separation OrderedSpectrum OrderedSpectrum.gap OrderedSpectrum.gap_ge_one total_spread_eq_endpoint_ratio HierarchySpec HierarchySpec.isJustified single_level_always_justified no_large_gap_single_level nearDecomposabilityParam simon_near_decomposable_gap decomposability_monotone crossBlockCoupling transaction_cost_reduces_coupling williamson_hierarchy_creation north_institutional_layering overlapWeight