Random forests and fermionic field theories
Kick-off event on Wed 29.10.25 at Institut Henri Poincaré. Inscriptions: link indico
The seminars at IHES will take place on the following Wednesdays: 12.11, 26.11 and 10.12, see program
Grassmann Calculus for the combinatorics of Spanning Trees and Forests
byAndrea Sportiello
Abstract:In this talk we will make a survey of how techniques of “Grassmann Calculus”, that is, integration of expressions involving anticommuting variables, provide fermionic analogues of Gaussian integration, Wick’s Theorem and perturbative field theory. These techniques are specially fruitful for describing certain combinatorial models in Statistical Mechanics, namely \(n=2\) Loop Models, Spanning Trees, and Spanning Forests.
If the time permits, we will also show how the model of Spanning Forests, in its Grassmann-variable formulation, has a hidden \(\mathrm{OSp}(1|2)\) supersymmetry, that, by the Parisi–Sourlas mechanism, implies that it must be in the same universality class of the \(O(n)\) loop model in the analytic continuation \(n\to-1\).
Mostly based on (old) works in collaboration with S. Caracciolo and A.D. Sokal.
All talks Fall '25: random forests and fermionic field theories