ﻻ يوجد ملخص باللغة العربية
We review a recently introduced effective graph approximation of causal dynamical triangulations (CDT), the multigraph ensemble. We argue that it is well suited for analytical computations and that it captures the physical degrees of freedom which are important for the reduction of the spectral dimension as observed in numerical simulations of CDT. In addition multigraph models allow us to study the relationship between the spectral dimension and the Hausdorff dimension, thus establishing a link to other approaches to quantum gravity
We study random walks on ensembles of a specific class of random multigraphs which provide an effective graph ensemble for the causal dynamical triangulation (CDT) model of quantum gravity. In particular, we investigate the spectral dimension of the
In this paper, we present a new framework to obtain tail inequalities for sums of random matrices. Compared with existing works, our tail inequalities have the following characteristics: 1) high feasibility--they can be used to study the tail behavio
We propose a $D$-dimensional generalization of $4D$ bi-scalar conformal quantum field theory recently introduced by G{u}rdogan and one of the authors as a strong-twist double scaling limit of $gamma$-deformed $mathcal{N}=4$ SYM theory. Similarly to t
The spectral flow is a classical notion of functional analysis and differential geometry which was given different interpretations as Fredholm index, Witten index, and Maslov index. The classical theory treats spectral flow outside the essential spec
We improve the recently discovered upper and lower bounds on the $O(1)$ correction to the Cardy formula for the density of states integrated over an energy window (of width $2delta$), centered at high energy in 2 dimensional conformal field theory. W