Survival Probability and Record Statistics for Random Walks

Explore survival probability and record statistics for random walks in this 49-minute lecture from the Erwin Schrödinger International Institute for Mathematics and Physics. Begin with a review of survival probability results for random walks and their application to record and extreme value statistics, including the universal Sparre-Andersen formula for continuous symmetric random walks. Delve into a model of random walk with correlated consecutive step signs, which maps onto the run-and-tumble particle model in certain parameter ranges. Examine the universal survival probability for this walk and its implications for record statistics, particularly in the scaling regime corresponding to run-and-tumble particles. Investigate extreme value statistics for this walk and compare findings to traditional random walk models. The lecture draws from collaborative work with F. Mori and references key publications in the field of random walk statistics and probability.