相关论文: Distances on the $\mathrm{CLE}_4$, critical Liouvi…

We initiate a study of the quasisymmetric uniformization of naturally arising random fractals and show that many of them fall outside the realm of quasisymmetric uniformization to simple canonical spaces. We begin with the trace, the graph…

In this paper we have calculated the spectral dimension of loop quantum gravity (LQG) using simple arguments coming from the area spectrum at different length scales. We have obtained that the spectral dimension of the spatial section runs…

A classical result of Nitsche \cite{Nit57} about the behaviour of the solutions to the Liouville equation $\Delta u=4 e^{2u}$ near isolated singularities is generalized to solutions of the Gaussian curvature equation $\Delta u=- \kappa(z)…

We study four dimensional quantum gravity formulated as a certain conformal field theory at the ultraviolet fixed point, whose dynamics is described by the combined system of Riegert-Wess-Zumino and Weyl actions. Background free nature…

The arguments were given in a number of our papers that the discrete quantum gravity based on the Regge calculus possesses nonzero vacuum expectation values of the triangulation lengths of the order of Plank scale $10^{-33}cm$. These…

We study a c=-2 conformal field theory coupled to two-dimensional quantum gravity by means of dynamical triangulations. We define the geodesic distance r on the triangulated surface with N triangles, and show that dim[r^{d_H}]= dim[N],…

This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed…

In a recent series of works, Miller and Sheffield constructed a metric on $\sqrt{8/3}$-Liouville quantum gravity (LQG) under which $\sqrt{8/3}$-LQG surfaces (e.g., the LQG sphere, wedge, cone, and disk) are isometric to their Brownian…

The proposed theory of causally structured discrete fields studies integer values on directed edges of a self-similar graph with a propagation rule, which we define as a set of valid combinations of integer values and edge directions around…

We provide first evidence that under certain conditions, 1/2-spin fermions may naturally behave like a Grover search, looking for topological defects in a material. The theoretical framework is that of discrete-time quantum walks (QW), i.e.…

We prove a shape theorem for internal diffusion limited aggregation on mated-CRT maps, a family of random planar maps which approximate Liouville quantum gravity (LQG) surfaces. The limit is an LQG harmonic ball, which we constructed in a…

We examine the relations between observables in two- and three-dimensional quantum gravity by studying the coupling of topologically massive gravity to matter fields in non-trivial representations of the three-dimensional Lorentz group. We…

We study the background scale independence in single-metric approximation to the functional renormalization group equation (FRGE) for quantum gravity and show that it is possible to formulate it without using higher-derivative gauge fixing…

The most obvious obstacle behind a direct test of Quantum Gravity (QG) is its energy scale ($10^{19}$ GeV), which remains well outside of any human made machine. The next best possible approach is to provide indirect tests on effective…

We show that for each ${\mathbf c}_{\mathrm M} \in [1,25)$, there is a unique metric associated with Liouville quantum gravity (LQG) with matter central charge ${\mathbf c}_{\mathrm M}$. An earlier series of works by…

It is argued that the quadruple gravitational constant 4G can be seen as a fundamental limit of nature. The limit holds across all gravitational systems and distinguishes bound from unbound systems. Including the maximum force c^4/4G allows…

We study SLE$_\kappa(\rho)$ curves, with $\kappa$ and $\rho$ chosen so that the curves hit the boundary. More precisely, we study the sets on which the curves collide with the boundary at a prescribed "angle" and determine the almost sure…

We consider the measure on multiple chordal Schramm-Loewner evolution ($SLE_\kappa$) curves. We establish a derivative estimate and use it to give a direct proof that the partition function is $C^2$ if $\kappa<4$.

The problem of background independent quantum gravity is the problem of defining a quantum field theory of matter and gravity in the absence of an underlying background geometry. Loop quantum gravity (LQG) is a promising proposal for…

The partition function of three dimensional gravity in the quantum regime is dual to the Ising model when the central charge $c=1/2$. Mathematically, we show that the three dimensional gravity can be described by Schramm-Loewner…