Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Speeding up non-Markovian First Passage Percolation with a few extra
  edges   One model of real-life spreading processes is First Passage Percolation (also
called SI model) on random graphs. Social interactions often follow bursty
patterns, which are usually modelled with i.i.d.~heavy-tailed passage times on
edges. On the other hand, random graphs are often locally tree-like, and
spreading on trees with leaves might be very slow, because of bottleneck edges
with huge passage times. Here we consider the SI model with passage times
following a power law distribution $\mathbb{P}(\xi>t)\sim t^{-\alpha}$, with
infinite mean. For any finite connected graph $G$ with a root $s$, we find the
largest number of vertices $\kappa(G,s)$ that are infected in finite expected
time, and prove that for every $k \leq \kappa(G,s)$, the expected time to
infect $k$ vertices is at most $O(k^{1/\alpha})$. Then, we show that adding a
single edge from $s$ to a random vertex in a random tree $\mathcal{T}$
typically increases $\kappa(\mathcal{T},s)$ from a bounded variable to a
fraction of the size of $\mathcal{T}$, thus severely accelerating the process.
We examine this acceleration effect on some natural models of random graphs:
critical Galton-Watson trees conditioned to be large, uniform spanning trees of
the complete graph, and on the largest cluster of near-critical
Erd\H{o}s-R\'enyi graphs. In particular, at the upper end of the critical
window, the process is already much faster than exactly at criticality.

21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int