75 citations · 932 across the 61 of their papers we have counts for
4 papers · 1 filter
Heat kernels on 2d Liouville quantum gravity: a numerical study
Grigory Bonik, Joe P. Chen, Alexander Teplyaev
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 ver…
Energy and Laplacian on Hanoi-type fractal quantum graphs
Patricia Alonso Ruiz, Daniel J. Kelleher, Alexander Teplyaev
This article studies potential theory and spectral analysis on compact metric spaces, which we refer to as fractal quantum graphs. These spaces can be represented as a (possibly in…
Gaps in the spectrum of the Laplacian on -Gaskets
Daniel Kelleher, Nikhar Gupta, Maxwell Margenot +3
This article develops analysis on fractal -gaskets, a class of post-critically finite fractals which include the Sierpinski triangle for , specifically properties of the L…
One-dimensional wave equations defined by fractal Laplacians
John Fun-Choi Chan, Sze-Man Ngai, Alexander Teplyaev
We study one-dimensional wave equations defined by a class of fractal Laplacians. These Laplacians are defined by fractal measures generated by iterated function systems with overl…