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Limit distributions of many-particle spectra and q-deformed Gaussian variables

Piotr Śniady — 2006

Banach Center Publications

We find the limit distributions for a spectrum of a system of n particles governed by a k-body interaction. The hamiltonian of this system is modelled by a Gaussian random matrix. We show that the limit distribution is a q-deformed Gaussian distribution with the deformation parameter q depending on the fraction k/√n. The family of q-deformed Gaussian distributions include the Gaussian distribution and the semicircular law; therefore our result is a generalization of the results of Wigner [Wig1,...

Dimensions of components of tensor products of representations of linear groups with applications to Beurling-Fourier algebras

Benoît Collins;  Hun Hee Lee;  Piotr Śniady — 2014

Studia Mathematica

We give universal upper bounds on the relative dimensions of isotypic components of a tensor product of representations of the linear group GL(n) and universal upper bounds on the relative dimensions of irreducible components of a tensor product of representations of the special linear group SL(n). This problem is motivated by harmonic analysis problems, and we give some applications to the theory of Beurling-Fourier algebras.

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