Related papers: Rigidity hierarchy in random point fields: random …
Regression methods are fundamental for scientific and technological applications. However, fitted models can be highly unreliable outside of their training domain, and hence the quantification of their uncertainty is crucial in many of…
This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…
We prove that the spectrum of the stochastic Airy operator is rigid in the sense of Ghosh and Peres (Duke Math. J., 166(10):1789--1858, 2017) for Dirichlet and Robin boundary conditions. This proves the rigidity of the Airy-$\beta$ point…
The Pearcey process is a universal point process in random matrix theory and depends on a parameter $\rho \in \mathbb{R}$. Let $N(x)$ be the random variable that counts the number of points in this process that fall in the interval…
A new type of dependent thinning for point processes in continuous space is proposed, which leverages the advantages of determinantal point processes defined on finite spaces and, as such, is particularly amenable to statistical, numerical,…
Natural systems are remarkably robust and resilient, maintaining essential functions despite variability, uncertainty, and hostile conditions. Understanding these nonlinear, dynamic behaviours is challenging because such systems involve…
Rigidity is an emergent property of materials - it is not a feature of individual components that comprise the structure, but instead arises from interactions between many constituent parts. Recently, it has been recognized that…
We consider stationary stochastic processes $X_n$, $n\in \mathbb{Z}$ such that $X_0$ lies in the closed linear span of $X_n$, $n\neq 0$; following Ghosh and Peres, we call such processes linearly rigid. Using a criterion of Kolmogorov, we…
In this paper, we establish a general setup for studying incidence-preserving motions of projective geometric configurations of points and lines via a "projective rigidity matrix". The spaces of infinitesimal motions of a point-line…
Designing fair algorithmic decision systems requires balancing model performance with fairness toward affected individuals: More fairness might require sacrificing some performance and vice versa, yet the space of possible trade-offs is…
Determinantal point processes (DPPs) are repulsive point processes where the interaction between points depends on the determinant of a positive-semi definite matrix. In this paper, we study the limiting process of L-ensembles based on…
Adding a column of numbers produces "carries" along the way. We show that random digits produce a pattern of carries with a neat probabilistic description: the carries form a one-dependent determinantal point process. This makes it easy to…
Determinantal point processes (DPPs) offer a powerful approach to modeling diversity in many applications where the goal is to select a diverse subset. We study the problem of learning the parameters (the kernel matrix) of a DPP from…
Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…
Determinantal point processes (DPPs) are point process models that naturally encode diversity between the points of a given realization, through a positive definite kernel $K$. DPPs possess desirable properties, such as exact sampling or…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
Robustness of decision rules to shifts in the data-generating process is crucial to the successful deployment of decision-making systems. Such shifts can be viewed as interventions on a causal graph, which capture (possibly hypothetical)…
As well as arising naturally in the study of non-intersecting random paths, random spanning trees, and eigenvalues of random matrices, determinantal point processes (sometimes also called fermionic point processes) are relatively easy to…
Determinantal point processes (DPPs) are repulsive point processes where the interaction between points depends on the determinant of a positive-semi definite matrix. The contributions of this paper are two-fold. First of all, we introduce…
We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the…