Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit determination of mean first-passage time for random walks on
  deterministic uniform recursive trees   The determination of mean first-passage time (MFPT) for random walks in
networks is a theoretical challenge, and is a topic of considerable recent
interest within the physics community. In this paper, according to the known
connections between MFPT, effective resistance, and the eigenvalues of graph
Laplacian, we first study analytically the MFPT between all node pairs of a
class of growing treelike networks, which we term deterministic uniform
recursive trees (DURTs), since one of its particular cases is a deterministic
version of the famous uniform recursive tree. The interesting quantity is
determined exactly through the recursive relation of the Laplacian spectra
obtained from the special construction of DURTs. The analytical result shows
that the MFPT between all couples of nodes in DURTs varies as $N \ln N$ for
large networks with node number $N$. Second, we study trapping on a particular
network of DURTs, focusing on a special case with the immobile trap positioned
at a node having largest degree. We determine exactly the average trapping time
(ATT) that is defined as the average of FPT from all nodes to the trap. In
contrast to the scaling of the MFPT, the leading behavior of ATT is a linear
function of $N$. Interestingly, we show that the behavior for ATT of the
trapping problem is related to the trapping location, which is in comparison
with the phenomenon of trapping on fractal T-graph although both networks
exhibit treestructure. Finally, we believe that the methods could open the way
to exactly calculate the MFPT and ATT in a wide range of deterministic media.

35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
1
The categories of this paper are: cs