In the book “Quantum Algorithms via Linear Algebra” I found this definition for the hitting time of a random walk:
$k$ giving $max_{u,v}|D(v) - A^l[u,v]| < \epsilon$ for all $l \geq k$ is called the hitting time.
Where $A$ is the walk matrix and $D$ is its stable distribution.
From my understanding, the hitting time for a start node $u$ and target $v$ is the minimum number of steps after which $v$ is hit starting from $u$.
How is this equivalent to the definition in the book, which I read as the minimum number of steps until the probability to reach $v$ from $u$ is almost the same as the probability of $v$ in the stable distribution?