Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long paths in first passage percolation on the complete graph I. Local
  PWIT dynamics   We study the random geometry of first passage percolation on the complete
graph equipped with independent and identically distributed edge weights,
continuing the program initiated by Bhamidi and van der Hofstad [9]. We
describe our results in terms of a sequence of parameters $(s_n)_{n\geq 1}$
that quantifies the extreme-value behavior of small weights, and that describes
different universality classes for first passage percolation on the complete
graph. We consider both $n$-independent as well as $n$-dependent edge weights.
The simplest example consists of edge weights of the form $E^{s_n}$, where $E$
is an exponential random variable with mean 1.
  In this paper, we investigate the case where $s_n\rightarrow \infty$, and
focus on the local neighborhood of a vertex. We establish that the
smallest-weight tree of a vertex locally converges to the invasion percolation
cluster on the Poisson weighted infinite tree. In addition, we identify the
scaling limit of the weight of the smallest-weight path between two uniform
vertices.

24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an