Stopping Times in Dynamics

Stopping times play an important role in areas of probability such as random walks on graphs and Markov chains theory. Important examples of stopping times include the hitting time (which records the first time to hit a particular part of the state space), cover time (which records the first time to have visited every state in the space) and blanket time (which records the first time that the empirical distribution of the random walk is, in a specific sense, close to the stationary distribution).

In this talk we will translate these concepts into the language of measure preserving dynamical systems, explore the relationships between them and discuss how they relate to the geometric measure theory properties of the dynamical system.