The zeros of random polynomials cluster uniformly near the unit circle
Hughes, C.P. ; Nikeghbali, A.
HAL, hal-00002972 / Harvested from HAL
Text on HAL
Given a sequence of random polynomials, we show that, under some very general conditions, the roots tend to cluster near the unit circle, and their angles are uniformly distributed. In particular, we do not assume independence or equidistribution of the coefficients of the polynomial. We apply this result to various problems in both random and deterministic sequences of polynomials, including some problems in random matrix theory.
Publié le : 2004-09-29
Classification:  Clustering of zeros,  Random polynomials,  30C15,  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 
@article{hal-00002972,
     author = {Hughes, C.P. and Nikeghbali, A.},
     title = {The zeros of random polynomials cluster uniformly near the unit circle},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00002972}
}

Hughes, C.P.; Nikeghbali, A. The zeros of random polynomials cluster uniformly near the unit circle. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00002972/