Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hitting times for second-order random walks   A second-order random walk on a graph or network is a random walk where
transition probabilities depend not only on the present node but also on the
previous one. A notable example is the non-backtracking random walk, where the
walker is not allowed to revisit a node in one step. Second-order random walks
can model physical diffusion phenomena in a more realistic way than traditional
random walks and have been very successfully used in various network mining and
machine learning settings. However, numerous questions are still open for this
type of stochastic processes. In this work we extend well-known results
concerning mean hitting and return times of standard random walks to the
second-order case. In particular, we provide simple formulas that allow us to
compute these numbers by solving suitable systems of linear equations.
Moreover, by introducing the "pullback" first-order stochastic process of a
second-order random walk, we provide second-order versions of the renowned
Kac's and random target lemmas.

28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys