相关论文: Subsequential scaling limits for Liouville graph d…

Using a stochastic control approach we establish couplings of the Liouville field and the sinh-Gordon field with the Gaussian free field in dimension $d=2$, such that the difference is in a Sobolev space of regularity $\alpha>1$. The…

The scaling behaviour of euclidean quantum gravity at an asymptotically safe critical point is studied by means of the exact renormalisation group. Gauge independence is ensured via a specific parameterisation of metric fluctuations…

The metric associated with the Liouville quantum gravity (LQG) surface has been constructed through a series of recent works and several properties of its associated geodesics have been studied. In the current article we confirm the…

We establish the first relationship between Schramm-Loewner evolution (SLE) and Liouville quantum gravity (LQG) in the supercritical (a.k.a. strongly coupled) phase, which corresponds to central charge values $\mathbf c_{\mathrm L} \in…

We study regular graphs whose distance-$2$ graph or distance-$1$-or-$2$ graph is strongly regular. We provide a characterization of such graphs $\Gamma$ (among regular graphs with few distinct eigenvalues) in terms of the spectrum and the…

We present an interesting reformulation of a collection of dilaton gravity models in two space-time dimensions into a field theory of two decoupled Liouville fields in flat space, in the presence of a Maxwell gauge field. An effective…

We characterize all connected graphs with second distance eigenvalue less than $-0.5858$.

We study the Euclidean path integral of two-dimensional quantum gravity with positive cosmological constant coupled to conformal matter with large and positive central charge. The problem is considered in a semiclassical expansion about a…

Liouville quantum gravity (LQG) is a one-parameter family of models of random fractal surfaces which first appeared in the physics literature in the 1980s. Recent works have constructed a metric (distance function) on an LQG surface. We…

Liouville quantum gravity (LQG) is, heuristically, a theory of random Riemannian geometry with Riemannian metric tensor $e^{\gamma h} (\mathrm{d} x^2 + \mathrm{d} y^2)$, where $h$ is a variant of the Gaussian free field and $\gamma > 0$ is…

We evaluate the three point function for arbitrary states in bosonic minimal models on the sphere coupled to quantum gravity in two dimensions. The validity of the formal continuation in the number of Liouville screening charge insertions…

We study a formulation of lattice gravity defined via Euclidean dynamical triangulations (EDT). After fine-tuning a non-trivial local measure term we find evidence that four-dimensional, semi-classical geometries are recovered at long…

We study the long range percolation model on $\mathbb{Z}$ where sites $i$ and $j$ are connected with probability $\beta |i-j|^{-s}$. Graph distances are now well understood for all exponents $s$ except in the case $s=2$ where the model…

We discuss some classical and quantum properties of 2d gravity models involving metric and a scalar field. Different models are parametrized in terms of a scalar potential. We show that a general Liouville-type model with exponential…

We consider the elliptic equation $-\Delta u = u^q|\nabla u|^p$ in $\mathbb R^n$ for any $p\ge 2$ and $q>0$. We prove a Liouville-type theorem, which asserts that any positive bounded solution is constant. The proof technique is based on…

We determine the spectrum and correlation functions of Liouville theory with a central charge less than (or equal) one. This completes the definition of Liouville theory for all complex values of the central charge. The spectrum is always…

This paper considers minimum-dimensional representations of graphs in pseudo-Euclidean spaces, where adjacency and non-adjacency relations are reflected in fixed scalar square values. A representation of a simple graph $(V,E)$ is a mapping…

Let $\Gamma$ be a compact metric graph, and denote by $\Delta$ the Laplace operator on $\Gamma$ with the first non-trivial eigenvalue $\lambda_1$. We prove the following Yang-Li-Yau type inequality on divisorial gonality $\gamma_{div}$ of…

This note provides a sufficient condition for linear lower bounds on chemical distances (compared to the Euclidean distance) in general spatial random graphs. The condition is based on the scarceness of long edges in the graph and weak…

We investigate the 1/8 BPS geometries with SU(2) x U(1) x SO(4) x R symmetry in IIB supergravity which were classified by Gava et al, (hep-th/0611065). It is desirable to have a complete set of differential equations imposed on the…