Informations pratiques sur cette ressource

Description de la ressource pédagogique

Description (résumé)

Stable matchings were introduced in a seminal paper by Gale and Shapley (1962) and play an important role in economics. Following closely Holroyd, Pemantle, Peres and Schramm (2009), we shall first discuss a few basic properties of stable matchings between two discrete point sets (resp. point processes) in Euclidean space, where the points prefer to be close to each other. For comparison we also discuss stable transports from Lebesgue measure to point processes. In the second part of the talk we consider a stable matching between the cubic lattice and a stationary Poisson process (or a determinantal point process) with higher intensity. The matched points form a stationary and ergodic (under lattice shifts) point process with unit intensity that has many remarkable properties. If the intensity of the Poisson process is close to one, then it very much resembles a Poisson process, while for large intensities it approaches the lattice. Moreover, the matched points form a hyperuniform and number rigid point process, in sharp contrast to a Poisson process. Still the pair correlation decays exponentially fast. The talk is based on joint work with M. Klatt and D. Yogeshwaran.

"Domaine(s)" et indice(s) Dewey

• Probabilités, Statistiques mathématiques, Mathématiques appliquées (519)

Thème(s)