We define a dynamical simple symmetric random walk in one dimension, and show that there almost surely exist exceptional times at which the walk tends to infinity. In fact the set of such times has Hausdorff dimension 1/2 almost surely. This is in contrast to the usual dynamical simple symmetric random walk in one dimension, for which such exceptional times are known not to exist. This is joint work with Martin Prigent.

**Date**: 28 October 2019, 12:00 (Monday, 3rd week, Michaelmas 2019)**Venue**: Mathematical Institute

Woodstock Road OX2 6GGSee location on maps.ox**Details**: L4**Speaker**: Matthew Roberts (University of Bath)**Organising department**: Department of Statistics**Organisers**: Christina Goldschmidt (Department of Statistics, University of Oxford), James Martin (Department of Statistics, University of Oxford)**Part of**: Probability seminar**Booking required?**: Not required**Audience**: Public- Editor: Christina Goldschmidt