17. Doktorand:innentreffen der Stochastik

Session

Session A3 Stochastics

4 Aug 2022, 09:00

HS 3 (Universität Klagenfurt)

Conveners

Session A3 Stochastics: Chair: Nils Heerten

• Patrick van Nerven (Uni Trier)
• Carolin Kleemann (Ruhr University Bochum)
• Kathrin Meier (Ruhr-University Bochum)

Contribution list Timetable

13. Sharp Constants in Normal an Edgeworth Approximation

04/08/2022, 09:00

Stochastics

Talk

We all know and love the central limit theorem (CLT) but there is a lot more to wish for. The Berry-Esseen theorem overestimates the actual error in the CLT and truly sharp error bounds for specific distributions are, as far as we are aware, only known in binomial cases and can be found in Schulz (2016). Even less seems to be known for other distances and higher-order approximations.

In...

7. Central limit theorems for generalized descents and generalized inversions in finite root systems

04/08/2022, 09:30

Stochastics

Talk

We start introducing generalized descents and generalized inversions in permutations as special cases of antichains and order ideals in the root poset for permutations. We provide the variance for generalized inversions and use a dependency graph method to conclude a central limit theorem for those and for antichains. We then generalize this result to antichains in root posets for finite Weyl...

32. Maximum interpoint distance of high-dimensional random vectors

04/08/2022, 10:00

Stochastics

Talk

A limit theorem for the largest interpoint distance of $p$ i.i.d. points on $\mathbb R^n$ to the Gumbel distribution is proven, where the number of points $p=p_n$ tends to infinity as the dimension of the points $n$ tends to infinity. The theorem holds under moment assumptions and corresponding assumptions on the rate of $p$. The proof is based on the Chen-Stein Poisson approximation method...