Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the concentration and the convergence rate with a moment condition in
  first passage percolation   We consider the first passage percolation model on the ${\bf Z}^d$ lattice.
In this model, we assign independently to each edge $e$ a non-negative passage
time $t(e)$ with a common distribution $F$. Let $a_{0,n}$ be the passage time
from the origin to $(n,0,..., 0)$. Under the exponential tail assumption,
  Kesten (1993) and Talagrand (1995) investigated the concentration of
$a_{0,n}$ from its mean using different methods. With this concentration and
the exponential tail assumption, Alexander gave an estimate for the convergence
rate for ${\bf E} a_{0,n}$. In this paper, focusing on a moment condition, we
reinvestigate the concentration and the convergence rate for $a_{0,n}$ using a
special martingale structure.

27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga