Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Emergent Space-Time via a Geometric Renormalization Method   We present a purely geometric renormalization scheme for metric spaces
(including uncolored graphs), which consists of a coarse graining and a
rescaling operation on such spaces. The coarse graining is based on the concept
of quasi-isometry, which yields a sequence of discrete coarse grained spaces
each having a continuum limit under the rescaling operation. We provide
criteria under which such sequences do converge within a superspace of metric
spaces, or may constitute the basin of attraction of a common continuum limit,
which hopefully, may represent our space-time continuum.
  We discuss some of the properties of these coarse grained spaces as well as
their continuum limits, such as scale invariance and metric similarity, and
show that different layers of spacetime can carry different distance functions
while being homeomorphic.
  Important tools in this analysis are the Gromov-Hausdorff distance functional
for general metric spaces and the growth degree of graphs or networks. The
whole construction is in the spirit of the Wilsonian renormalization group.
  Furthermore we introduce a physically relevant notion of dimension on the
spaces of interest in our analysis, which e.g. for regular lattices reduces to
the ordinary lattice dimension. We show that this dimension is stable under the
proposed coarse graining procedure as long as the latter is sufficiently local,
i.e. quasi-isometric, and discuss the conditions under which this dimension is
an integer. We comment on the possibility that the limit space may turn out to
be fractal in case the dimension is non-integer. At the end of the paper we
briefly mention the possibility that our network carries a translocal far-order
which leads to the concept of wormhole spaces and a scale dependent dimension
if the coarse graining procedure is no longer local.

23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom