Equidistribution of zeros of random polynomials

نویسندگان

  • Igor E. Pritsker
  • Koushik Ramachandran
چکیده

We study the asymptotic distribution of zeros for the random polynomials Pn(z) = ∑n k=0 AkBk(z), where {Ak}k=0 are non-trivial i.i.d. complex random variables. Polynomials {Bk}k=0 are deterministic, and are selected from a standard basis such as Szegő, Bergman, or Faber polynomials associated with a Jordan domain G bounded by an analytic curve. We show that the zero counting measures of Pn converge almost surely to the equilibrium measure on the boundary of G if and only if E[log |A0|] <∞.

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عنوان ژورنال:
  • Journal of Approximation Theory

دوره 215  شماره 

صفحات  -

تاریخ انتشار 2017