Calendar

Posted February 28, 2026

Probability Seminar Questions or comments?

Leo Tyrpak, University of Oxford
Fluctuations of spatial population models with non-local interactions

We analyse a class of spatial population models where the branching rate of particles depends non-locally on the whole empirical measure of particles. Scaling limits of this model have previously been shown to include the non-local Fisher-KPP equation and the porous medium equation. In this talk we will discuss the fluctuations of the process around these deterministic limits. We will show how an understanding of these can be applied to quantify the impact on geographical distance on genetic distance in the spirit of the classical Wright-Malecot formula.

Posted March 19, 2026

Probability Seminar Questions or comments?

Aditya Guntuboyina, University of California, Berkeley
What functions does XGBoost learn?

XGBoost is a scalable tree boosting system that is widely used by data scientists for regression. We develop a theoretical framework that explains what kinds of functions XGBoost is able to learn. We introduce an infinite-dimensional function class that extends ensembles of shallow decision trees, along with a natural measure of complexity that generalizes the regularization penalty built into XGBoost. We show that this complexity measure aligns with classical notions of variation—in one dimension it corresponds to total variation, and in higher dimensions it is closely tied to a well-known concept called Hardy–Krause variation. We prove that the best least-squares estimator within this class can always be represented using a finite number of trees, and that it achieves a nearly optimal statistical rate of convergence, avoiding the usual curse of dimensionality. Our work provides the first rigorous description of the function space that underlies XGBoost, clarifies its relationship to classical ideas in nonparametric estimation, and highlights an open question: does the actual XGBoost algorithm itself achieve these optimal guarantees? This is joint work with Dohyeong Ki at UC Berkeley.

Posted March 30, 2026

Probability Seminar Questions or comments?

Olga Iziumtseva, University of Nottingham
Self-intersection local times of Volterra Gaussian processes in stochastic flows with interaction

In this talk, we discuss the existence of multiple self-intersection local times for stochastic processes $x(u(s),t), s\in [0,1]$, where $u$ is a Volterra Gaussian process and $x$ is the solution to the equation with interaction driven by the occupation measure of the process $u$. It appears that self-intersection local times for the process $x(u(s),t), s\in[0,1]$ can be defined as weighted self-intersection local times for the process $u$. We present conditions on Volterra Gaussian processes and weight functions sufficient for the existence of weighted self-intersection local times for a large class of unbounded weights. This is a joint work with Wasiur R. Khudabukhsh

Posted April 7, 2026

Probability Seminar Questions or comments?

Wasiur KhudaBukhsh, University of Nottingham
A probabilistic view on perturbations of the identity operator

Perturbation analysis of operators is a classical topic in functional analysis. In this talk, we will look at perturbations of the identity operator from a probabilistic perspective in which the identity operator corresponds to the Wiener process. It is well known that the three functionals of the Wiener trajectories, namely, the time of the maxima, the amount of time spent in the positive half of the real line, and the time of the last zero, follow the arcsine law. We provide an elementary proof of the universality of the arcsine laws when the identity operator is perturbed by an absolutely continuous operator in $L_2([0, 1])$.