Philippe Biane (Université Marne-la-Vallée)
Tuesday, May 17, 2022 - 13:45
HU Berlin, Institut für Physik, IRIS-Haus
Zum Großen Windkanal 2, 12489 Berlin-Adlershof, Raum 1.007,
Hybrid seminar: Algebra, Geometry and Physics (HU Berlin/MPIM Bonn)
The Quantum Symmetric Simple Exclusion Process (QSSEP) is a model of fermionic quantum particles hopping on a finite interval. D. Bernard and T. Jin have shown that the fluctuations of the invariant measure for this process, when the number of sites goes to infinity, are encoded into polynomials, with a strong combinatorial flavour. In this talk I give an explicit combinatorial formula for these polynomials in terms of associahedra which, quite surprisingly, shows that they can be interpreted as free cumulants of a family of commuting random variables. I will explain the physical model in the talk as well as what are free cumulants, which are fundamental quantities in non-commutative versions of probability theory.
submitted by Gaetan Borot (