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Cumulants of the q-semicircular law, Tutte polynomials, and heaps
Discrete Mathematics & Theoretical Computer Science
International audience The q-semicircular law as introduced by Bożejko and Speicher interpolates between the Gaussian law and the semicircular law, and its moments have a combinatorial interpretation in terms of matchings and crossings. We prove that the cumulants of this law are, up to some factor, polynomials in q with nonnegative coefficients. This is done by showing that they are obtained by an enumeration of connected matchings, weighted by the evaluation at (1,q) of a Tutte polynomial.doi:10.46298/dmtcs.3074 fatcat:tudzzs5ju5bnxoikdvqd3x5rv4