Heat kernel fluctuations have been observed in some random walks in random environments. In this talk, I will consider the three-dimensional uniform spanning tree (UST) as a random environment. I will first show the occurrence of log-logarithmic fluctuations around the leading order for the volume of intrinsic balls in the UST. This is then used to obtain similar fluctuations for the quenched heat kernel.

**Date**: 14 November 2022, 12:00 (Monday, 6th week, Michaelmas 2022)**Venue**: Mathematical Institute

Woodstock Road OX2 6GGSee location on maps.ox**Details**: L5**Speaker**: Satomi Watanabe (Kyoto)**Organising department**: Department of Statistics**Part of**: Probability seminar**Booking required?**: Not required**Audience**: Public- Editor: Christina Goldschmidt