Related papers: Comments on "Modelling the gap size distribution o…

Physicists routinely need probabilistic models for a number of tasks such as parameter inference or the generation of new realizations of a field. Establishing such models for highly non-Gaussian fields is a challenge, especially when the…

The Random Parameters model was proposed to explain the structure of the covariance matrix in problems where most, but not all, of the eigenvalues of the covariance matrix can be explained by Random Matrix Theory. In this article, we…

We point out that the method presented in a recent arXiv article by Jia et al. (arXiv:2512.21848) for constructing local hidden-state models closely follows the framework we developed in N. von Selzam & F. Marquardt (PRX Quantum, 2025) for…

During the attempt to line up into a dense traffic people have necessarily to share a limited space under turbulent conditions. From the statistical point view it generally leads to a probability distribution of the distances between the…

We study a variant of the R\'enyi parking problem in which car length is repeatedly halved and determine the rate at which the remaining space decays.

Autonomous vehicles (AV) look set to become common on our roads within the next few years. However, to achieve the final breakthrough, not only functional progress is required, but also satisfactory safety assurance must be provided. Among…

In these talks, I discuss a few selected topics in integrable models that are of interest from various points of view. Some open questions are also described.

In the classical parking problem, unit intervals ("car lengths") are placed uniformly at random without overlapping. The process terminates at saturation, i.e. until no more unit intervals can be stowed. In this paper, we present a…

We generalize the recent study of random space-filling bearings to a more realistic situation, where the spacing offset varies randomly during the space-filling procedure, and show that it reproduces well the size-distributions observed in…

Transit agencies have been removing a large number of bus stops, but discussions around the bus stop spacings exhibit a lack of clarity and data for comparison. This paper proposes new terminology and concepts for statistical consideration…

In the Page parking (or packing) model on a discrete interval (also known as the discrete R{\'e}nyi packing problem or the unfriendly seating problem), cars of length two successively park uniformly at random on pairs of adjacent places,…

This paper proposes an extensive overview of safety applications and approaches as it relates to automated driving from the prospectives of sensor configurations, vehicle dynamics modelling, tyre modeling, and estimation approaches. First,…

Motivated by ride-sharing platforms' efforts to reduce their riders' wait times for a vehicle, this paper introduces a novel problem of placing vehicles to fulfill real-time pickup requests in a spatially and temporally changing…

Model criticism is usually carried out by assessing if replicated data generated under the fitted model looks similar to the observed data, see e.g. Gelman, Carlin, Stern, and Rubin [2004, p. 165]. This paper presents a method for latent…

In general, the distribution of residuals cannot be obtained explicitly. We give an asymptotic formula for the density of Pearson residuals in continuous generalized linear models corrected to order $n^{-1}$, where $n$ is the sample size.…

This work builds on the notion of record of rooted trees. We provide an alternative definition of parking functions, derive from it a record-preserving bijection between rooted trees and parking functions, and establish a join…

Different families of models first developed for fluid mechanics have been extended to road, pedestrian, or intracellular transport. These models allow to describe the systems at different scales and to account for different aspects of…

Short-term future of automated driving can be imagined as a hybrid scenario in which both automated and human-driven vehicles co-exist in the same environment. In order to address the needs of such road configuration, many technology…

In shared space environments, urban space is shared among different types of road users, who frequently interact with each other to negotiate priority and coordinate their trajectories. Instead of traffic rules, interactions among them are…

We investigate the gap formation probability of the effective one dimensional gas model proposed the energy level statistics for disordered solids.