Related papers: Rigidity hierarchy in random point fields: random …
We construct families of rational functions $f \colon \bP^1_k \to \bP^1_k$ of degree $d \geq 2$ over a perfect field $k$ whose associated fixed-point processes fail to be martingales. Conversely, for any normal variety $X \subset…
This paper deals with the scenario approach to robust optimization. This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in the parameters of an optimization problem. Solving the resulting…
We introduce the notion of a random relaxed asymptotic contraction in the setting of random normed modules. The contraction condition employs two quasi-metrics that are built directly from the random operator: a lower quasi-metric which…
Our first result states that the orthogonal and symplectic Bessel processes are rigid in the sense of Ghosh and Peres. Our argument in the Bessel case proceeds by an estimate of the variance of additive statistics in the spirit of Ghosh and…
The main result of this paper, Theorem 1.5, establishes a conjecture of Lyons and Peres: for a determinantal point process governed by a reproducing kernel, the system of kernels sampled at the particles of a random configuration is…
Many problems in systems and control theory can be formulated in terms of robust D-stability analysis, which aims at verifying if all the eigenvalues of an uncertain matrix lie in a given region D of the complex plane. Robust D-stability…
We study a point process describing the asymptotic behavior of sizes of the largest components of the random graph G(n,p) in the critical window p=n^{-1}+lambda n^{-4/3}. In particular, we show that this point process has a surprising…
The Marginally Rigid State is a candidate paradigm for what makes granular material a state of matter distinct from both liquid and solid. Coordination number is identified as a discriminating characteristic, and for rough-surfaced…
We show the existence of rigid combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, $t$-designs, and $t$-wise…
Randomized smoothing has shown promising certified robustness against adversaries in classification tasks. Despite such success with only zeroth-order access to base models, randomized smoothing has not been extended to a general form of…
Position determination in biological systems is often achieved through protein concentration gradients. Measuring the local concentration of such a protein with a spatially-varying distribution allows the measurement of position within the…
This paper proposes strategies for designing a system whose computational model is subject to aleatory and epistemic uncertainty. Aleatory variables, which are caused by randomness in physical parameters, are draws from a possibly unknown…
We consider stationary configurations of points in Euclidean space which are marked by positive random variables called scores. The scores are allowed to depend on the relative positions of other points and outside sources of randomness.…
This paper studies random operator-valued positive definite (p.d.) kernels and their connection to moment dilations. A class of random p.d. kernels is introduced in which the positivity requirement is imposed only in expectation, extending…
A system comprised of an elastic solid and its response to an external random force sequence is shown to behave based on the principles of the theory of algorithmic complexity and randomness. The solid distorts the randomness of an input…
A determinantal point process (DPP) is a probabilistic model of set diversity compactly parameterized by a positive semi-definite kernel matrix. To fit a DPP to a given task, we would like to learn the entries of its kernel matrix by…
Determinantal point processes (DPPs) have recently proved to be a useful class of models in several areas of statistics, including spatial statistics, statistical learning and telecommunications networks. They are models for repulsive (or…
We study the robustness of system estimation to parametric perturbations in system dynamics and initial conditions. We define the problem of sensitivity-based parametric uncertainty quantification in dynamical system estimation. The main…
Randomized Numerical Linear Algebra (RandNLA) uses randomness to develop improved algorithms for matrix problems that arise in scientific computing, data science, machine learning, etc. Determinantal Point Processes (DPPs), a seemingly…
Neural networks (NNs) are now routinely implemented on systems that must operate in uncertain environments, but the tools for formally analyzing how this uncertainty propagates to NN outputs are not yet commonplace. Computing tight bounds…