Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cover time for branching random walks on regular trees   Let $T$ be the regular tree in which every vertex has exactly $d\ge 3$
neighbours. Run a branching random walk on $T$, in which at each time step
every particle gives birth to a random number of children with mean $d$ and
finite variance, and each of these children moves independently to a uniformly
chosen neighbour of its parent. We show that, starting with one particle at
some vertex $0$ and conditionally on survival of the process, the time it takes
for every vertex within distance $r$ of $0$ to be hit by a particle of the
branching random walk is almost surely $r + \frac{2}{\log(3/2)}\log\log r +
o(\log\log r)$.

24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph