Heat kernels on 2d Liouville quantum gravity: a numerical study
arXiv:1411.1738
Abstract
We numerically compute the heat kernel on a square lattice torus equipped with the measure corresponding to Liouville quantum gravity (LQG). From the on-diagonal heat kernel we verify that the spectral dimension of LQG is 2. Furthermore, when diffusion is started from a high point of the underlying Gaussian free field, our numerics indicates superdiffusive space-time scaling with respect to the Euclidean metric in the small space-to-time regime. The implications of this result require further investigation, but seem to coincide with the notion that the Euclidean metric is not the right geodesic for characterizing the geometry of LQG.
arXiv commentPreliminary report
References in corpus (6)
- Energy measures and indices of Dirichlet forms, with applications to derivatives on some fractals
- KPZ formula derived from Liouville heat kernel
- Liouville heat kernel: regularity and bounds
- On the heat kernel and the Dirichlet form of Liouville Brownian Motion
- Diffusion in planar Liouville quantum gravity
- Continuity and estimates of the Liouville heat kernel with applications to spectral dimensions