Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Wasserstein Distance Between $k$-Step Probability Measures on
  Finite Graphs   We consider random walks $X,Y$ on a finite graph $G$ with respective
lazinesses $\alpha, \beta \in [0,1]$. Let $\mu_k$ and $\nu_k$ be the $k$-step
transition probability measures of $X$ and $Y$. In this paper, we study the
Wasserstein distance between $\mu_k$ and $\nu_k$ for general $k$. We consider
the sequence formed by the Wasserstein distance at odd values of $k$ and the
sequence formed by the Wasserstein distance at even values of $k$. We first
establish that these sequences always converge, and then we characterize the
possible values for the sequences to converge to. We further show that each of
these sequences is either eventually constant or converges at an exponential
rate. By analyzing the cases of different convergence values separately, we are
able to partially characterize when the Wasserstein distance is constant for
sufficiently large $k$.

10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
9
The categories of this paper are: nlin