Department of Mathematical Statistics, Royal Institute of Technology
A person's portrait
project title

Log-correlated fields and applications to statistical mechanics.

funded by

Ragnar Söderbergs stiftelse

How can we understand complex systems? This is the overarching question for Gaultier Lambert’s research project. More specifically, he wants to understand the physics of certain materials such as quantum semi-conductors and spin glasses (i.e. glasses with special magnetic characteristics).

Lambert works within the field of probability theory, a field at the interface of mathematics and physics, with broad applications both in natural and social science. This research field has gained interest from the public since professor Giorgio Parisi received the Nobel Prize in Physics in 2021 for “the discovery of the interplay of disorder and fluctuations in physical systems from atomic to planetary scales”.


Lambert aims to develop a general understanding of the fluctuations of a special class of complex systems called logarithmically correlated fields. They are models of random surfaces with a fractal geometry, which arise in the mathematical theories of spin glasses developed by Parisi. There are many fascinating mathematical challenges to study the geometry of these random surfaces. If they exhibit universal features this would mean that the macroscopic (large scale) properties of such complex systems are completely independent of the underlying microscopic (small scale) structure of the model. Lambert’s goal is to study the statistical properties of logarithmically correlated fields and develop new techniques for probability theory in high-dimensions. He believes that such methods will also be important in other contexts outside his own project.

Photo: Tobias Björkgren

March 2023

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