Stochastics for big data and big systems - bridging local and global

Research Project, 2013 – 2018

This project will develop general mathematics and statistics for understanding and modeling complex structures in time, space and networks. We will explore connectivity and phase transition for very large systems, develop theory which shows how normal behavior changes and becomes extreme, provide methods to understand the effects which small and local perturbations have on systems, and solve difficult and important optimization problems. The key will be to understand how local properties influence global behavior, and vice versa. As one example: how do the local structures of a gel and small local perturbations of these structures determine global characteristics, such as drug delivery through the gel? The amazing generality of mathematics will make our answers to questions about one kind of structure, like this one, help us describe and understand quite different structures. Our theory will model the temperature distribution in a heat wave, the structure of pores in soil, the spread of opinion in a social network, the optimal path for a traveling salesman, and structures of many other and quite different kinds. We will use the new theory to contribute to modeling in geotechnology and medicine, to lessen the impact of extreme floods and windstorms in a changing climate, to safety and efficiency of marine transports, to avoidance of car accidents, and to planning of telecommunication networks. The project group combines a unique array of skills in extreme values, Gaussian processes, discrete probability, abstract optimization, and spatial statistics. It has a worldwide network of collaborators, and interest and experience in using mathematics to solve problems in science and technology, and has made important contributions to the project area. The 2011 Swedish Research Council evaluation of Mathematics in Sweden described our Stochastic Centre (earlier funded by the Wallenberg foundation) as outstanding and as one of the strongest groups in the world. The project will develop new ways of working together which use the opportunities which lie in our different knowledge and approaches and our large network of collaborators – and the possibilities for free and unfettered research given by the Wallenberg grant – for groundbreaking progress. A strategic result will be a Swedish intellectual infrastructure which can exploit three great opportunities of the future: Big Data, Big Systems and Big Progress of Theory.

Participants

Funding

Related Areas of Advance and Infrastructure

Sustainable development

Driving Forces

Publications

An Analysis of the Induced Linear Operators Associated to Divide and Color Models

Mixing time for random walk on supercritical dynamical percolation

Divide and color representations for threshold Gaussian and stable vectors

A formula for hidden regular variation behavior for symmetric stable distributions

A few surprising integrals

Generalized Divide and Color models

Finite element approximation of Lyapunov equations for the computation of quadratic functionals of SPDEs

Quenched exit times for random walk on dynamical percolation

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