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The purpose of the present paper is to establish explicit bounds on moderate deviation probabilities for a rather general class of geometric functionals enjoying the stabilization property, under Poisson input and the assumption of a…
Matrix stiffness expressions are derived for the particle movements in an assembly of rigid granules having compliant contacts. The derivations include stiffness terms that arise from the particle shapes at their contacts. These geometric…
We establish tightness of graph-based stochastic processes in the space $D[0+\epsilon,1-\epsilon]$ with $\epsilon >0$ that allows for discontinuities of the first kind. The graph-based stochastic processes are based on statistics…
Studying the effects of one-way variation of any number of parameters on any number of output probabilities quickly becomes infeasible in practice, especially if various evidence profiles are to be taken into consideration. To provide for…
We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of…
We study limiting properties of ratios of ordered points of point processes whose intensity measures have regularly varying tails, giving a systematic treatment which points the way to "large-trimming" properties of extremal processes and a…
In this paper, we develop a general machinery for finding explicit uniform probability and moment bounds on sub-additive positive functionals of random processes. Using the developed general technique, we derive uniform bounds on the…
The problem is sequence prediction in the following setting. A sequence $x_1,...,x_n,...$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, it is required…
Local decision rules are commonly understood to be more explainable, due to the local nature of the patterns involved. With numerical optimization methods such as gradient boosting, ensembles of local decision rules can gain good predictive…
3D Computer simulations and experiments are employed to study random packings of compressible spherical grains under external confining stress. Of particular interest is the rigid ball limit, which we describe as a continuous transition in…
Previous approaches to robustness in natural language processing usually treat deviant input by relaxing grammatical constraints whenever a successful analysis cannot be provided by ``normal'' means. This schema implies, that error…
The Ginibre point process is given by the eigenvalue distribution of a non-hermitian complex Gaussian matrix in the infinite matrix-size limit. This is a determinantal point process (DPP) on the complex plane ${\mathbb{C}}$ in the sense…
We consider the problem of estimating the density $\Pi$ of a determinantal process $N$ from the observation of $n$ independent copies of it. We use an aggregation procedure based on robust testing to build our estimator. We establish…
We introduce and study a class of determinantal probability measures generalising the class of discrete determinantal point processes. These measures live on the Grassmannian of a real, complex, or quaternionic inner product space that is…
Regression tasks, notably in safety-critical domains, require proper uncertainty quantification, yet the literature remains largely classification-focused. In this light, we introduce a family of measures for total, aleatoric, and epistemic…
We extend the restrictiveness measure of Fudenberg, Gao & Liang (2026) to functional and structural econometric settings using Gaussian process priors. We find that models evaluated over continuum domains appear more restrictive than when…
Causal rigid particles whose action includes an {\it arbitrary} dependence on the world-line extrinsic curvature are considered. General classes of solutions are constructed, including {\it causal tachyonic} ones. The Hamiltonian…
Random spanning trees are among the most prominent determinantal point processes. We give four examples of random spanning trees on ladder-like graphs whose rungs form stationary renewal processes or regenerative processes of order two,…
Gaussian Processes (GPs) are widely employed in control and learning because of their principled treatment of uncertainty. However, tracking uncertainty for iterative, multi-step predictions in general leads to an analytically intractable…
The bulk scaling limit of eigenvalue distribution on the complex plane ${\mathbb{C}}$ of the complex Ginibre random matrices provides a determinantal point process (DPP). This point process is a typical example of disordered hyperuniform…