Seminarium Nieliniowość i Geometria

Motivated by the theory of orthogonal random matrix ensembles, we investigate the integrable semi-discrete hierarchy of the Pfaff lattice. With the use of a mapping connecting this system with the Toda lattice (related to the unitary ensemble), we derive the initial datum for the first flow of Pfaff. This initial datum provides the most natural approach for constructing the continuum limit, while also suggesting a natural reduction of the system. Interestingly, both the semi-discrete system and the hydrodynamic chain emerging in the continuum limit reduce to the same novel semi-discrete system. The talk is based on the work in collaboration with C. Benassi and A. Moro (https://doi.org/10.48550/arXiv.2504.11296).