# Student Probability Seminar

#### Ageing, stable subordinators and the emergence of the arcsine law

**Speaker:**
Lisa Hartung

**Location:**
Warren Weaver Hall 805

**Date:**
Thursday, February 15, 2018, 11 a.m.

**Synopsis:**

*This talk will link the three keywords in the title. **The term ageing can be understood as follows. Assume a systems is prepared (produced) at some initial time t_0. Then the system is left to itself. After some time t_w (called waiting time), an experimentalist may perform some measurement on the system. The question is, whether the experimentalist will be able to deduce the elapsed waiting time from his observation. **To understand the above question in a toy model I’ll first explain a fundamental limit theorems for sums of random variables in a regime where the limit is a stable subordinator. This regime can be understood as “the maximal summands dominate the whole sum”. Then I’ll explain in a simple random energy model why the so called ‘clock process’ satisfies exactly this limit theorem and how it is related to ‘ageing’. Finally, we will understand how the arcsine enters the picture.*