Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Determining global mean-first-passage time of random walks on Vicsek
  fractals using eigenvalues of Laplacian matrices   The family of Vicsek fractals is one of the most important and
frequently-studied regular fractal classes, and it is of considerable interest
to understand the dynamical processes on this treelike fractal family. In this
paper, we investigate discrete random walks on the Vicsek fractals, with the
aim to obtain the exact solutions to the global mean first-passage time
(GMFPT), defined as the average of first-passage time (FPT) between two nodes
over the whole family of fractals. Based on the known connections between FPTs,
effective resistance, and the eigenvalues of graph Laplacian, we determine
implicitly the GMFPT of the Vicsek fractals, which is corroborated by numerical
results. The obtained closed-form solution shows that the GMFPT approximately
grows as a power-law function with system size (number of all nodes), with the
exponent lies between 1 and 2. We then provide both the upper bound and lower
bound for GMFPT of general trees, and show that leading behavior of the upper
bound is the square of system size and the dominating scaling of the lower
bound varies linearly with system size. We also show that the upper bound can
be achieved in linear chains and the lower bound can be reached in star graphs.
This study provides a comprehensive understanding of random walks on the Vicsek
fractals and general treelike networks.

9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg