Chaos and the economy

A system is generally termed chaotic in the world on a large scale if minor causes can have major effects. The weather is an excellent example. Because the larger world is made up of small things, however, it is important to ask whether chaotic behaviour on the large scale has its origins in the smaller world. This is a very difficult question to answer, since the two worlds are subject to very different natural laws. In the world of the small, the laws of quantum mechanics apply.

Somewhat simplified, complex systems are systems which cannot be understood by taking traditional approaches. Often, the attributes of the system change constantly in unpredictable ways. In some cases, complex systems can be modelled by assuming some attributes of the system to be random within certain limits. This random matrices theory helps to significantly reduce the number of system variables in the outcome. The research group uses this theory in many different areas of physics.

Interesting – and important – complex systems are not only found in traditional physics but also in the economy, for example the financial markets. Physicists can make a considerable contribution to exploring such systems – albeit only because a lot of data and quantitative information is available. Here the group was able to quantify the dramatic effects of the mutual dependencies of borrowers on the risk to lenders. This inherent risk appears to have been massively underestimated in the years prior to the financial crisis. Unfortunately, physics and mathematics have been moving apart for several decades. The Guhr research group deals with problems which are currently significant in both physics and mathematics, specifically applying supersymmetry to solve our statistical models. In mathematics, the normal numbers commute; in other words, 3 • 4 = 4 • 3. However, anticommuting variables also exist, for which it applies that a • b = −b • a. Surprisingly, these two types of variables can be used together so as to significantly reduce the ­effective number of variables in certain statistical models.