Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the fastest finite Markov processes   Consider a finite irreducible Markov chain with invariant probability $\pi$.
Define its inverse communication speed as the expectation to go from x to y,
when x, y are sampled independently according to $\pi$. In the discrete time
setting and when $\pi$ is the uniform distribution $\upsilon$, Litvak and Ejov
have shown that the permutation matrices associated to Hamiltonian cycles are
the fastest Markov chains. Here we prove (A) that the above optimality is with
respect to all processes compatible with a fixed graph of permitted transitions
(assuming that it does contain a Hamiltonian cycle), not only the Markov
chains, and, (B) that this result admits a natural extension in both discrete
and continuous time when $\pi$ is close to $\upsilon$: the fastest Markov
chains/processes are those moving successively on the points of a Hamiltonian
cycle, with transition probabilities/jump rates dictated by $\pi$.
Nevertheless, the claim is no longer true when $\pi$ is significantly different
from $\upsilon$.

11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an