# Michel Talagrand receives Abel Prize

The French mathematician Michel Talagrand was honoured this year with the Abel Prize "for his groundbreaking contributions to probability theory and functional analysis, with outstanding applications in mathematical physics and statistics."

Matthias Löwe, Professor of Stochastics at Mathematics Münster, gives a brief insight into the prizewinner's work:

Michel Talagrand is an extraordinarily productive mathematician (at this point he has published about 300 papers, including quite a few books), working on various questions in probability theory.

Perhaps his best-known work deals with the concentration of measure phenomenon: a quantity that depends on a large number of random influences is constant to first approximation. At an elementary level, this has been known for more than 300 years as the "law of large numbers". For example, if you toss a coin very often and measure the relative frequency of the event that the coin shows "heads", then this relative frequency approaches the probability of "heads". The law of large numbers is the reason why something like probability exists at all and why taking large samples in statistics I meaningful.

In his work on measure concentration, Talagrand generalises this phenomenon to a large class of random phenomena and provides bounds on how quickly the approximation to the mean occurs. This work has many applications, for example in the analysis of the performance of algorithms, the investigation of combinatorial questions or systems in physics known as "spin glasses" (which are also analysed as simple models for memories). In the early 1980s, the physicist Giorgio Parisi (Nobel Prize 2021) established a heuristics about certain spin glass models, which Talagrand proved 25 years later in a ground-breaking paper.

At the Cluster of Excellence Mathematics Münster, Talagrand's inequalities for measure concentration are used in the probability theory working groups. In particular, one working group also deals with spin glasses, where Talagrand's work is an incentive to understand the complex world of these models even better.

**What is the Abel-Prize?**

The Abel Prize is an international honour awarded annually since 2003 by the Norwegian Academy of Sciences for scientific work of exceptional depth and influence in the field of mathematics. It is named after the Norwegian mathematician Niels Henrik Abel and is endowed with 7.5 million Norwegian kroner, i.e. around 650,000 euros.