  We establish and generalise several bounds for various random walk quantities
including the mixing time and the maximum hitting time. Unlike previous
analyses, our derivations are based on rather intuitive notions of local
expansion properties which allows us to capture the progress the random walk
makes through $t$-step probabilities.
  We apply our framework to dynamically changing graphs, where the set of
vertices is fixed while the set of edges changes in each round. For random
walks on dynamic connected graphs for which the stationary distribution does
not change over time, we show that their behaviour is in a certain sense
similar to static graphs. For example, we show that the mixing and hitting
times of any sequence of $d$-regular connected graphs is $O(n^2)$, generalising
a well-known result for static graphs. We also provide refined bounds depending
on the isoperimetric dimension of the graph, matching again known results for
static graphs. Finally, we investigate properties of random walks on dynamic
graphs that are not always connected: we relate their convergence to
stationarity to the spectral properties of an average of transition matrices
and provide some examples that demonstrate strong discrepancies between static
and dynamic graphs.
