Events Calendar
Jan 23
14:00 - 15:00
Mathematical Physics & Integrable Systems seminar: Tamara Grava (University of Bristol & SISSA, Trieste, Italy)
SMSAS Mathematical Physics seminars
Orthogonal polynomials on the complex plane for a class of measure with discrete rotational symmetry

Abstract

We study the asymptotic behaviour of   orthogonal polynomials   on the complex plane for a measure with discrete rotational symmetry. Such model originates from normal matrix models. We show that the orthogonality on the plane can be reduced to an orthogonality relation on a contour of the complex plane. We then obtain the asymptotic expansion of the orthogonal polynomials as the degree N goes to infinity. According to the values of the parameters in the measure, three different asymptotic regimes are present: 1) the zeros of the polynomials accumulate in the large N limit   on a single closed contour; 2) the zeros of the polynomials accumulate in the large N limit on several close and disconnected contours; 3) there is a the transition regime between case 1) and 2) that is described via a Painlevé IV equation.

Location

SR2,
Sibson Building (SibSR2)
United Kingdom
Map

Details

Open to All interested persons,

Contact: Dr Pavlos Xenitidis
E: P.Xenitidis@kent.ac.uk
School of Mathematics, Statistics and Actuarial Science

 

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Last Updated: 10/01/2012