- Series
- Analysis Seminar
- Time
- Wednesday, December 7, 2011 - 2:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Andrei Martinez Finkelshtein – University of Almeria, Spain – andrei@ual.es
- Organizer
- Jeff Geronimo
The asymptotic analysis of orthogonal polynomials with respect to a
varying weight has found many interesting applications in
approximation theory, random matrix theory and other areas. It has
also stimulated a further development of the logarithmic potential
theory, since the equilibrium measure in an external field associated
with these weights enters the leading term of the asymptotics and its
support is typically the place where zeros accumulate and oscillations
occur.
In a rather broad class of problems the varying weight on the real
line is given by powers of a function of the form exp(P(x)), where P
is a polynomial. For P of degree 2 the associated orthogonal
polynomials can be expressed in terms of (varying) Hermite
polynomials. Surprisingly, the next case, when P is of degree 4, is
not fully understood. We study the equilibrium measure in the external
field generated by such a weight, discussing especially the possible
transitions between different configurations of its support.
This is a joint work with E.A. Rakhmanov and R. Orive.