## Probability in the North East day

#### 14 June 2023

**Organizers: ** Nic Freeman.

**Venue: **University of Sheffield. All talks will be held in LT 9 on Floor H of the Hicks Building. Lunch and coffee will be held in Room 15 on Floor I.

Attendence is free but registration is **required for organisational purposes**, by emailing Nic Freeman
by Wednesday 7th June 2023.

Please indicate any special dietary requirements you may have.

## Programme

For large and local large deviations for sums of i.i.d. real-valued random variables in the domain of attraction of an $\alpha$-stable law with $\alpha$ in (0,2], there are two different scenarios: either the deviation is realised via a collective behaviour with all summands contributing to the deviation (a Gaussian scenario), or a single summand is atypically large and contributes to the deviation (a one-big-jump scenario). Such results are known when alpha in (0,2) or when $\alpha=2$ and the random variables admit a moment of order $2+\delta$ for some $\delta>0$ with the right-tail probability regularly varying.

This talk will present new results extending the above known phenomenon to the last missing case including where $\alpha=2$ and the right tail is regularly varying with index -2. Threshold for the phase transition between the Gaussian and the one-big-jump regimes will be identified and applications will be discussed.