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

*A
project supported by the Knut and Alice Wallenberg foundation*

**Summary**** : **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.

**The
group**

Holger Rootzén (Extreme value stochastics, leader)

Aila Särkkä (Spatial statistics, vice leader)

Robert Berman (Complex analysis)

Olle Häggström (Discrete probability)

Johan Jonasson (Combinatorial probability)

Rebecka Jörnsten (High-dimensional data
analysis)h

Igor Rychlik (Stochastic processes for
material fatigue and marine safety)

Jeff Steif (Discrete probability)

Bernt Wennberg (Interacting particle systems,
Bolzmann equation)

Johan Wästlund (Optimization in random
models)

Sergei Zuyev
(Spatial stochastics)