Wioletta Ruszel - Fermionic Gaussian free field and connections to random lattice models

May 21, 2024
Recorded 21 May 2024. Wioletta Ruszel of Utrecht University presents "Fermionic Gaussian free field and connections to random lattice models" at IPAM's Vertex Models: Algebraic and Probabilistic Aspects of Universality Workshop. Abstract: In this talk we will first give a gentle introduction into determinantal and permanental point processes and explain connections to objects from physics which are called fermionic and bosonic variables. Fermions do not like to be close together like electrons in an atom and boson like each other like protons in the kernel of an atom. The classical discrete Gaussian free field is a multivariate Gaussian distribution with a specific covariance structure. The fermionic version of that is related and can be expressed in terms of fermionic variables. We will show some examples and properties of those objects and finally relate them to the degree field of a uniform spanning tree and height-1 field of the Abelian sandpile model if time permits. This is joint work with L. Chiarini (DUR), A. Cipriani (UCL) and A. Rapoport (UU) Learn more online at: