Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multi-scale Lipschitz percolation of increasing events for Poisson
  random walks   Consider the graph induced by $\mathbb{Z}^d$, equipped with uniformly
elliptic random conductances. At time $0$, place a Poisson point process of
particles on $\mathbb{Z}^d$ and let them perform independent simple random
walks. Tessellate the graph into cubes indexed by $i\in\mathbb{Z}^d$ and
tessellate time into intervals indexed by $\tau$. Given a local event
$E(i,\tau)$ that depends only on the particles inside the space time region
given by the cube $i$ and the time interval $\tau$, we prove the existence of a
Lipschitz connected surface of cells $(i,\tau)$ that separates the origin from
infinity on which $E(i,\tau)$ holds. This gives a directly applicable and
robust framework for proving results in this setting that need a multi-scale
argument. For example, this allows us to prove that an infection spreads with
positive speed among the particles.

27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat