Analysis Seminar

We obtain a new asymptotic expansion of the orthogonal polynomials in the context of exponentially varying weights. This goes beyond the classical works of Carleman and Suetin, where the domain was fixed and the weight as well ("hard-edge"). Here, the domain is obtained implicitly from the problem using an energy approach, or alternatively from an obstacle problem. As a consequence, we obtain the boundary universality law for soft edges, given by the error function. This reports on joint work with A. Wennman.