Asymptotics of symmetric polynomials with applications to statistical mechanics and representation theory (Q5746112)

The authors develop a method for studying the limit, as the number of variables tends to infinity, of symmetric polynomials arising in the context of representation theory as well as in its application to probability and statistical mechanics. Applications of the computational technique presented are also given; in particular, in the field of representation theory, to the approximation of characters of \(U(\infty)\) as well as of its \(q\)-deformed characters. Other applications concern the behaviour of uniformly random lozenge tilings of large polygonal domains and the GUE-eigenvalues distribution in the limit; the asymptotic behavior, as the size tends to infinity, of a functional of the alternating sign matrices of size \(n\), which describe the configurations of the six-vertex model with domain wall b.c.'s; the asymptotic expansions of the boundary-to-boundary current for the completely packed \(O(n=1)\) dense loop model.