Related papers: Multigraph models for causal quantum gravity and s…
Causal Dynamical Triangulations (CDT) is a methodology to define and compute the gravitational path integral, whose aim is a fully fledged nonperturbative quantum field theory of gravity and spacetime. Analogous to lattice formulations of…
We investigate the genuinely quantum features of continuous-time quantum walks by combining a single-time and a multi-time quantifier of nonclassicality. On the one hand, we consider the quantum-classical dynamical distance…
The continuous-time quantum walk on the underlying graphs of association schemes have been studied, via the algebraic combinatorics structures of association schemes, namely semi-simple modules of their Bose-Mesner and (reference state…
The statistical properties of dynamically triangulated manifolds (DT mfds) in terms of the geodesic distance have been studied numerically. The string susceptibility exponents for the boundary surfaces in three-dimensional DT mfds were…
Four-dimensional CDT (causal dynamical triangulations) is a lattice theory of geometries which one might use in an attempt to define quantum gravity non-perturbatively, following the standard procedures of lattice field theory. Being a…
The dynamically triangulated random surface (DTRS) approach to Euclidean quantum gravity in two dimensions is considered for the case of the elemental building blocks being quadrangles instead of the usually used triangles. The well-known…
We show that for three dimensional gravity with higher genus boundary conditions, if the theory possesses a sufficiently light scalar, there is a second order phase transition where the scalar field condenses. This three dimensional version…
Random walks on regular bounded degree expander graphs have numerous applications. A key property of these walks is that they converge rapidly to the uniform distribution on the vertices. The recent study of expansion of high dimensional…
Within the causal dynamical triangulations approach to the quantization of gravity, striking evidence has emerged for the dynamical reduction of spacetime dimension on sufficiently small scales. Specifically, the spectral dimension…
Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterisation of empirical data.…
The paper considers the spectral determinant of quantum graph families with chaotic classical limit and no symmetries. The secular coefficients of the spectral determinant are found to follow distributions with zero mean and variance…
Random walks on a graph reflect many of its topological and spectral properties, such as connectedness, bipartiteness and spectral gap magnitude. In the first part of this paper we define a stochastic process on simplicial complexes of…
Causal Dynamical Triangulations is a background independent approach to quantum gravity. In this paper we introduce a phenomenological transfer matrix model, where at each time step a reduced set of quantum states is used. The states are…
We extend the definition of "spectral dimension" (usually defined for fractal and lattice geometries) to theories on smooth spacetimes with anisotropic scaling. We show that in quantum gravity dominated by a Lifshitz point with dynamical…
We study the scale dependence of the twist-3 quark-gluon parton distributions using the observation that in the multi-color limit the corresponding QCD evolution equations possess an additional integral of motion and turn out to be…
We investigate the validity of the "Einstein relations" in the general setting of unimodular random networks. These are equalities relating scaling exponents: $d_w = d_f + \tilde{\zeta}$ and $d_s = 2 d_f/d_w$, where $d_w$ is the walk…
Building upon [1], this study aims to introduce fractal geometry into graph theory, and to establish a potential theoretical foundation for complex networks. Specifically, we employ the method of substitution to create and explore…
We establish spectral theorems for random walks on mapping class groups of connected, closed, oriented, hyperbolic surfaces, and on $\text{Out}(F_N)$. In both cases, we relate the asymptotics of the stretching factor of the…
This topical review gives a comprehensive overview and assessment of recent results in Causal Dynamical Triangulations (CDT), a modern formulation of lattice gravity, whose aim is to obtain a theory of quantum gravity nonperturbatively from…
It is well known that many real world networks have the power-law degree distribution (scale-free property). However there are no rigorous results for continuous-time quantum walks on such realistic graphs. In this paper, we analyze…