Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral dimension in graph models of causal quantum gravity   The phenomenon of scale dependent spectral dimension has attracted special
interest in the quantum gravity community over the last eight years. It was
first observed in computer simulations of the causal dynamical triangulation
(CDT) approach to quantum gravity and refers to the reduction of the spectral
dimension from 4 at classical scales to 2 at short distances. Thereafter
several authors confirmed a similar result from different approaches to quantum
gravity. Despite the contribution from different approaches, no analytical
model was proposed to explain the numerical results as the continuum limit of
CDT. In this thesis we introduce graph ensembles as toy models of CDT and show
that both the continuum limit and a scale dependent spectral dimension can be
defined rigorously. First we focus on a simple graph ensemble, the random comb.
It does not have any dynamics from the gravity point of view, but serves as an
instructive toy model to introduce the characteristic scale of the graph, study
the continuum limit and define the scale dependent spectral dimension. Having
defined the continuum limit, we study the reduction of the spectral dimension
on more realistic toy models, the multigraph ensembles, which serve as a radial
approximation of CDT. We focus on the (recurrent) multigraph approximation of
the two-dimensional CDT whose ensemble measure is analytically controlled. The
latter comes from the critical Galton-Watson process conditioned on
non-extinction. Next we turn our attention to transient multigraph ensembles,
corresponding to higher-dimensional CDT. Firstly we study their fractal
properties and secondly calculate the scale dependent spectral dimension and
compare it to computer simulations. We comment further on the relation between
Horava-Lifshitz gravity, asymptotic safety, multifractional spacetimes and
CDT-like models.

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The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: stat