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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

### Holger Rootzen (contact)

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

### Robert Berman

Chalmers, Mathematical Sciences, Algebra and geometry

### Olle Häggström

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

### Johan Jonasson

Chalmers, Mathematical Sciences, Analysis and Probability Theory

### Rebecka Jörnsten

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

### Igor Rychlik

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

### Aila Särkkä

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

### Jeffrey Steif

Chalmers, Mathematical Sciences, Analysis and Probability Theory

### Johan Wästlund

Chalmers, Mathematical Sciences, Analysis and Probability Theory

### Bernt Wennberg

Chalmers, Mathematical Sciences

### Sergey Zuev

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

## Funding

### Knut and Alice Wallenberg Foundation

Project ID: KAW2012,0067

Funding Chalmers participation during 2013–2018

## Related Areas of Advance and Infrastructure

### Sustainable development

Driving Forces

## Publications

**2021**

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

**Journal article**