Titolo: Discrete geometric structure of large-scale interacting systems
Abstract.
In
this talk, we explore large-scale interacting systems that explain
macroscopic phenomena through the movement of microscopic particles.
These systems are modeled by discrete lattices where microscopic
dynamics occur and the transitions between adjacent sites, referred to
as “interactions” in our definition. We classify interactions based on
conserved quantities, which reflect macroscopic properties, and
introduce wedge sums and box products as methods to construct new
interactions from existing ones. We also present a discrete harmonic
theory for large-scale interacting systems on discrete lattices with
finite local state sets. By assuming exchangeable interactions, we
define the inverse harmonic period matrix, which we expect to correspond
to the diffusion matrix in the hydrodynamic limit. Our result offers an
interpretation of the diffusion matrix based on the geometry of the
microscopic model. Founded by the European Union - Next Generation EU.