Related papers: From Trees to Gravity
The search for scale-invariant random geometries is central to the Asymptotic Safety hypothesis for the Euclidean path integral in quantum gravity. In an attempt to uncover new universality classes of scale-invariant random geometries that…
In this short note we review a recently found formulation of two-dimensional causal quantum gravity defined through Causal Dynamical Triangulations and stochastic quantization. This procedure enables one to extract the nonperturbative…
Geometry of networks endowed with a causal structure is discussed using the conventional framework of equilibrium statistical mechanics. The popular growing network models appear as particular causal models. We focus on a class of tree…
This thesis is driven by a central question: "What can we learn from random geometries about the structure of quantum spacetime?" In Chapter 2, we provide a partial review of the mathematical foundation of this thesis, random geometry. In…
By appropriate scaling of coupling constants a one-parameter family of ensembles of two-dimensional geometries is obtained, which interpolates between the ensembles of (generalized) causal dynamical triangulations and ordinary dynamical…
We describe the idea of studying quantum gravity by means of dynamical triangulations and give examples of its implementation in 2, 3 and 4 space time dimensions. For $d=2$ we consider the generic hermitian 1-matrix model. We introduce the…
We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of 2D quantum gravity which works away from…
The central topic of this thesis is two dimensional Quantum Gravity and its properties. The term Quantum Gravity itself is ambiguous as there are many proposals for its correct formulation and none of them have been verified experimentally.…
In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short…
We consider fixed-point equations for probability measures charging measured compact metric spaces that naturally yield continuum random trees. On the one hand, we study the existence/uniqueness of the fixed-points and the convergence of…
We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a…
It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum…
We present a simple yet rigorous approach to the determination of the spectral dimension of random trees, based on the study of the massless limit of the Gaussian model on such trees. As a byproduct, we obtain evidence in favor of a new…
The search for a mathematical foundation for the path integral of Euclidean quantum gravity calls for the construction of random geometry on the spacetime manifold. Following developments in physics on the two-dimensional theory, random…
A number of recent proposals for a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. There are two fundamental challenges to any such…
Investigating quantum gravity requires a comprehension of both, general relativity and quantum field theory. Therefore this thesis starts, after a general introduction to the treated topics, with a brief review of the field theoretical…
An outstanding challenge for models of non-perturbative quantum gravity is the consistent formulation and quantitative evaluation of physical phenomena in a regime where geometry and matter are strongly coupled. After developing appropriate…
We study the diffusion equation in two-dimensional quantum gravity, and show that the spectral dimension is two despite the fact that the intrinsic Hausdorff dimension of the ensemble of two-dimensional geometries is very different from…
A potentially powerful approach to quantum gravity has been developed over the last few years under the name of Causal Dynamical Triangulations. Numerical simulations have given very interesting results in the cases of two, three and four…
We examine the scaling of geodesic correlation functions in two-dimensional gravity and in spin systems coupled to gravity. The numerical data support the scaling hypothesis and indicate that the quantum geometry develops a non-perturbative…