Permutation invariant matrix models and the statistics of words

par George Barnes (Queen Mary U. of London)

mercredi 10 mars 2021, 14:00 → 15:00 Europe/Paris

https://greenlight.lal.cloud.math.cnrs.fr/b/fab-49u-gkt

In recent work Kartsaklis, Ramgoolam and Sadrzadeh developed a class of Gaussian matrix models for which the usual U(N) symmetry is relaxed to a less restrictive S_N, the group of permutations. Utilising the combinatorics of Wick contractions from QFT and representation theory helps to uncover the rich mathematical structure of these models and permits the computation of expectation values of the most general permutation invariant Gaussian theories. An application of these models to the statistics of words in computational linguistics is described. This application was central in motivating the development of these models and, more recently, provided the stimulus for extending this programme to general permutation invariant Gaussian two-matrix models.