A natural question in statistical physics and ergodic optimization is to understand how a complex system under weak interactions can be ordered when the temperature decreases. Ground states are measures obtained as limits of Gibbs measures by letting the temperature goes to zero. Minimizing configurations are typical configurations of the ground states. The objectives of the group is to study these objects on different examples, the Frenkel-Kontorova model, subshifts of finite type on lattices over an infinite alphabet, intermittent maps or more generally non-uniformly hyperbolic systems, non-autonomous product of matrices, or random dynamical systems. The ultimate goal is to understand the possibility of the emergence of aperiodic structures.
Research tasks
- FKM: Frenkel-Kontorova model
- Task GGM: Gradient Gibbs measures
- Task MGS: Multidimensional Ground States
- Task TDS : Thermodynamic of Delone Sets
- Task LCM: Low Complexity Model
- Task EOT: Ergodic Optimization Theory
- Task RDS: Random Dynamical Systems
