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Quantum symmetric simple exclusion process, associahedra and free cumulants

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Philippe Biane (Alg. Geom. Phys. seminar, talk online only)
Université Marne-la-Vallee
Tue, 17/05/2022 - 13:45 - 15:30

Online talk only. Contact: Gaetan Borot (HU Berlin)  

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.

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