A measure of similarity or overlap between different configurations or individuals appears in many complex systems such as spin glasses, evolving populations, optimization problems and neural networks. In the context of spin glasses, the concept was introduced by Edwards and Anderson 50 years ago and gives a measure of similarity between pairs of spin configurations. In the context of evolving populations, the overlap measures the similarity between genomes of individuals.
In general the overlaps fluctuate and have non-trivial statistics. Giorgio Parisi's replica theory of mean field spin glasses predicted a universal form for the overlap statistics. In this talk the speaker will compare these predictions with the statistics for different models of disordered systems and for evolving populations.
About the speaker: Professor Bernard Derrida studied Physics at the École Normale Supérieure in Paris from 1971 to 1975 and obtained his French Doctorat d’État from Université d’Orsay in 1979. He worked in the Theory Group at Saclay from 1979 to 1993 and became Professor at Université Pierre et Marie Curie and at the École Normale Supérieure in 1993. Since 2015, he has been Professor of Statistical Physics at the Collège de France in Paris. He is a member of the French Academy of Sciences.
Prof. Derrida has made pioneering contributions to statistical physics, particularly to the theory of disordered systems and non-equilibrium systems. His best-known works include the introduction of the Random Energy Model, one of the simplest models of spin glasses, and a series of exact solutions to problems involving exclusion processes and persistence phenomena.
His outstanding contributions have been recognized through several prestigious international distinctions. He was awarded the Boltzmann Medal in 2010, became Chevalier de la Légion d’honneur in 2017, and served as the Solvay Chair of Physics in Brussels in 2018. In 2022, he was awarded the Aisenstadt Chair at the Centre de recherches mathématiques (CRM), Université de Montréal. In 2026, he was awarded the Dirac Medal of the International Centre for Theoretical Physics (ICTP), one of the most prestigious international honours in theoretical physics, in recognition of his contributions to statistical mechanics.
This lecture is part of the program "Two and a half decades of the Macroscopic Fluctuation Theory"