Airy point process via supersymmetric lifts

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 Schur functions multivariate Bessel functions. obtain explicit expressions class lifts inspired by determinantal due \cite{MJ03}. Asymptotic analysis enable us probe edge. focus several settings where Airy point process arises.