Randomness that drives growth fronts

Associate Professor Daniel Ahlberg will receive funding from the Knut and Alice Wallenberg Foundation to recruit an international researcher for a postdoctoral position at the Department of Mathematics, Stockholm University.

Probability distributions describing the effects of randomness are at the heart of statistical mathematics. The most well-known is the normal distribution, the Gaussian bell curve. The wide occurrence of the normal distribution is explained by the central limit theorem, which shows that the bell curve can be expected by an entity consisting of many small and roughly independent parts. Although the bell curve describes many random processes, both in society and in nature, there are many random phenomena that follow other laws, and mathematicians seek an explanation for their occurrence.

One pioneering step was taken in the mid-1980s by physicists Mehran Kardar, Giorgio Parisi and Yi-Cheng Zhang. Empirical studies have shown that their differential equation (the KPZ equation) describes the evolution over time of the frontier of a growing interface in random spatial processes, such as bacterial growth or a burning sheet of paper. Understanding the emergence of phenomena related to the KPZ equation constitutes one of the main directions in the study of random spatial growth, which is the subject of the planned project.

Deviations from Gaussian behavior, which is predicted by the KPZ equation, is in statistical physics characteristic of critical behavior. One of the main goals of this project is to understand how the underlying geometry contributes to this deviating behavior. One way to address this problem is to explore geodesics (curves that provide the shortest path between two points) and the central role they play in understanding properties of the associated metric space. In this way the project hopes to increase the understanding of how complex phenomena observed in random spatial growth arise.

Photo: Tiffany Y Y Lo