Related papers: Hyperuniform random measures, transport and rigidi…
This paper conducts sensitivity analysis of random constraint and variational systems related to stochastic optimization and variational inequalities. We establish efficient conditions for well-posedness, in the sense of robust Lipschitzian…
The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures. This paper includes eight sections. Section 1 is a longer introduction, which gives a…
We review some recent developments which make use of the concept of `superstatistics', an effective description for nonequilibrium systems with a varying intensive parameter such as the inverse temperature. We describe how the asymptotic…
A recent paper by Cordero-Erausquin and Klartag provides a characterization of the measures $\mu$ on $\R^d$ which can be expressed as the moment measures of suitable convex functions $u$, i.e. are of the form $(\nabla u)\_\\#e^{- u}$ for…
This work focuses on the bearing rigidity theory, namely the branch of knowledge investigating the structural properties necessary for multi-element systems to preserve the inter-units bearings when exposed to deformations. The original…
Decision making under uncertainty is a cross-cutting challenge in science and engineering. Most approaches to this challenge employ probabilistic representations of uncertainty. In complicated systems accessible only via data or black-box…
As a generic model for transport of interacting fermions through a barrier or interstitials in a lattice, quantum Brownian motion in a periodic potential is studied. There is a duality transformation between the continuous coordinate or…
We consider a generalization of the weighted random ball model. The model is driven by a random Poisson measure with a product heavy tailed intensity measure. Such a model typically represents the transmission of a network of stations with…
The robustness of properties of a statistical physics model to slight perturbations in the exact local interactions of the model is a very relevant philosophical question, considering real-life measurements on which we base some models can…
The paper is devoted to a comprehensive study of composite models in variational analysis and optimization the importance of which for numerous theoretical, algorithmic, and applied issues of operations research is difficult to overstate.…
The concept of metastate measures on the states of a random spin system was introduced to be able to treat the large-volume asymptotics for complex quenched random systems, like spin glasses, which may exhibit chaotic volume dependence in…
Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…
In this work, we define the notion of unimodular random measured metric spaces as a common generalization of various other notions. This includes the discrete cases like unimodular graphs and stationary point processes, as well as the…
The study of finite approximations of probability measures has a long history. In (Xu and Berger, 2017), the authors focus on constrained finite approximations and, in particular, uniform ones in dimension $d=1$. The present paper gives an…
Hyperuniformity, which is a type of long-range order that is characterized by the suppression of long-range density fluctuations in comparison to the fluctuations in standard disordered systems, has emerged as a powerful concept to aid in…
Optimal sample path properties of stochastic processes often involve generalized H\"{o}lder- or variation norms. Following a classical result of Taylor, the exact variation of Brownian motion is measured in terms of $\psi (x) \equiv $…
We study notions of hyperuniformity for invariant locally square-integrable point processes in regular trees. We show that such point processes are never geometrically hyperuniform, and if the diffraction measure has support in the…
We prove that, for a $C^2$ partially hyperbolic endomorphism of the 2-torus which is strongly transitive, given an ergodic $u$-Gibbs measure that has positive center Lyapunov exponent and has full support, then either the map is special…
Hyperuniform materials, characterized by their suppressed density fluctuations and vanishing structure factors as the wave number approaches zero, represent a unique state of matter that straddles the boundary between order and randomness.…
The stability of solutions to optimal transport problems under variation of the measures is fundamental from a mathematical viewpoint: it is closely related to the convergence of numerical approaches to solve optimal transport problems and…