Related papers: Random Fixed Points, Limits and Systemic risk
The goal of this paper is to clarify when the solutions to stochastic partial differential equations stay close to a given subset of the state space for starting points which are close as well. This includes results for deterministic…
In this paper, we resolve the computational complexity of a number of outstanding open problems with practical applications. Here is the list of problems we show to be PPAD-complete, along with the domains of practical significance:…
In this paper we systematically study various properties of the distance graph in ${\Bbb F}_q^d$, the $d$-dimensional vector space over the finite field ${\Bbb F}_q$ with $q$ elements. In the process we compute the diameter of distance…
The paper analyses the convergence of the $p$-version of the FEM when the solution is piecewise analytic function. It focuses on pointwise convergence of the gradient. It shows that at boundary the rate is different than inside the element…
This systemic risk paper introduces inhomogeneous random financial networks (IRFNs). Such models are intended to describe parts, or the entirety, of a highly heterogeneous network of banks and their interconnections, in the global financial…
In this paper, we introduce and analyze a new low-rank multilevel strategy for the solution of random diffusion problems. Using a standard stochastic collocation scheme, we first approximate the infinite dimensional random problem by a…
Elliptic boundary value problems which are posed on a random domain can be mapped to a fixed, nominal domain. The randomness is thus transferred to the diffusion matrix and the loading. While this domain mapping method is quite efficient…
This paper surveys recent analytical and numerical research on linear problems for the integral fractional Laplacian, fractional obstacle problems, and fractional minimal graphs. The emphasis is on the interplay between regularity,…
This paper catalogues a variety of examples concerning a type of function of a $p$-adic integer variable defined by a formal series expression we have dubbed "$\mathcal{F}$-series". These series exhibit a new, previously undocumented form…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously…
This two-part paper details a theory of solvability for the power flow equations in lossless power networks. In Part I, we derive a new formulation of the lossless power flow equations, which we term the fixed-point power flow. The model is…
We investigate the distribution of eigenvalues of weighted adjacency matrices from a specific ensemble of random graphs. We distribute $N$ vertices across a fixed number $\kappa$ of components, with asymptotically $\alpha_j \dot N$ vertices…
Samples of dynamic or time-varying networks and other random object data such as time-varying probability distributions are increasingly encountered in modern data analysis. Common methods for time-varying data such as functional data…
Stochastic domains often involve risk-averse decision makers. While recent work has focused on how to model risk in Markov decision processes using risk measures, it has not addressed the problem of solving large risk-averse formulations.…
Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show…
Static packings of frictional rigid particles are investigated by means of discrete element simulations. We explore the ensemble of allowed force realizations in the space of contact forces for a given packing structure. We estimate the…
We identify the stochastic processes associated with one-sided fractional partial differential equations on a bounded domain with various boundary conditions. This is essential for modelling using spatial fractional derivatives. We show…
We consider the problem of measuring the margin of robust feasibility of solutions to a system of nonlinear equations. We study the special case of a system of quadratic equations, which shows up in many practical applications such as the…
We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complete graph with vertices as the points of $A \subseteq…