  Random walks have been intensively studied on regular and complex networks,
which are used to represent pairwise interactions. Nonetheless, recent works
have demonstrated that many real-world processes are better captured by
higher-order relationships, which are naturally represented by hypergraphs.
Here, we study random walks on hypergraphs. Due to the higher-order nature of
these mathematical objects, one can define more than one type of walks. In
particular, we study the unbiased and the maximal entropy random walk on
hypergraphs, emphasizing their similarities and differences. We characterize
these processes through their stationary distributions and the associated
hitting times, which we obtain analytically. To illustrate our findings, we
present a toy example and conduct extensive analyses of artificial and real
hypergraphs, providing insights into both their structural and dynamical
properties. We hope that our findings motivate further research extending the
analysis to different classes of random walks as well as to practical
applications.
