Absolute relaxation time (source code)

= Absolute relaxation time
{title2=$t_{\mathrm{rel},*}=1/\gamma_*$}

For a finite <irreducible Markov chain> with at least two states that is an <aperiodic Markov chain> and a <reversible Markov chain>, put $\gamma_*=1-\max_{j\geq2}|\lambda_j|$ and $t_{\mathrm{rel},*}=1/\gamma_*$. This is the reciprocal of the <absolute L2 spectral gap of a reversible Markov chain>. It agrees with the reciprocal of the ordinary <spectral gap> $1-\lambda_2$ for a <lazy Markov chain>, but need not agree when there are negative <eigenvalues>.