TV Distance to Stationary Distribution
Theory & Spectral Data
Directed Laplacian:
L = D_out − A (row-normalized: P = D⁻¹A)
Stationary: πP = π, π1 = 1
Mixing time: t_mix ≈ log(n/ε) / gap
Spectral gap = 1 − |λ₂| of row-stochastic P
Perron-Frobenius: unique stationary dist.
iff digraph is strongly connected + aperiodic
Nodes—
Steps taken0
Spectral gap—
TV distance—
Strongly conn.—