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.
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.