Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Philippe Biane (Alg. Geom. Phys. seminar, talk online only)
Affiliation:

Université Marne-la-Vallee
Date:

Tue, 17/05/2022 - 13:45 - 15:30 Online talk only. Contact: Gaetan Borot (HU Berlin)

https://hu-berlin.zoom.us/j/61686623112 [3]

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.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/10472

[3] https://hu-berlin.zoom.us/j/61686623112