Abstract:
Stable looptrees are a class of random fractal objects that arise as scaling limits of critical percolation boundaries on random planar maps. In this talk, we will use a resistance metric to give a construction of Brownian motion on stable looptrees, and prove that it arises as a scaling limit of discrete-time simple random walks on discrete looptrees. We will then use geometric arguments to give precise estimates on its heat kernel, in both the quenched and annealed regimes. This can also be used to give asymptotics for its associated eigenvalue counting function.
Biography:
I am a final year PhD student at the University of Warwick, and am currently visiting Kyoto University as a JSPS Research Fellow.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai