We study the local asymptotics at edge for particle systems arising from: (i) eigenvalues of sums unitarily invariant random Hermitian matrices and (ii) signatures corresponding to decompositions tensor products representations unitary group. Our method treats these two models in parallel, is based on new formulas observables described terms a special family lifts, which we call supersymmetric ...

Our study is initiated by a multi-component particle system underlying the tiling of a half hexagon by three species of rhombi. In this particle system species j consists of ⌊j/2⌋ particles which are interlaced with neigbouring species. The joint probability density function (PDF) for this particle system is obtained, and is shown in a suitable scaling limit to coincide with the joint eigenvalu...

The Witten–Kontsevich theorem states that a certain generating function for intersection numbers on the moduli space of stable curves is a tau-function for the KdV integrable hierarchy. This generating function can be recovered via the topological recursion applied to the Airy curve x = 1 2 y 2. In this paper, we consider the topological recursion applied to the irregular spectral curve xy2 = 2...

This paper follows upon the study of the Airy bispectral involution made in [KR]. There we gave an analogue, for arbitrary rank, of the rank-one bispectral involution developed by Wilson [W1]. Recently, [W2], Wilson has established a relationship between the rank-one bispectral involution and the complex analogue of the CalogeroMoser phase space. This relationship leads to explicit formulae for...

The effective action for light mesons in the external uniform static electromagnetic fields was obtained on the basis of QCD string theory. We imply that in the presence of light quarks the area law of the Wilson loop integral is valid. The approximation of the Nambu-Goto straight-line string is used to simplify the problem. The Coulomb-like short-range contribution which goes from one-gluon ex...