Abstract
EXPECTED ZEROS OF RANDOM ORTHOGONAL POLYNOMIALS ON THE REAL LINE
*Pralipta Rout and Dr. P. K. Mishra
ABSTRACT
We study the expected number of zeros for random linear combination of orthogonal polynomials with respect to measures supported on the real line. The counting measures of zeros for these random polynomials converge weakly to the corresponding equilibrium measures from potential theory. We quantify this convergence and obtain asymptotic results on the expected number of zeros located in various sets of plane. Random coefficients may be dependent and need not have identical distributions in our results.
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