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- W2097079886 abstract "We identify the scaling region of a width O(n^{-1}) in the vicinity of the accumulation points $t=pm 1$ of the real roots of a random Kac-like polynomial of large degree n. We argue that the density of the real roots in this region tends to a universal form shared by all polynomials with independent, identically distributed coefficients c_i, as long as the second moment sigma=E(c_i^2) is finite. In particular, we reveal a gradual (in contrast to the previously reported abrupt) and quite nontrivial suppression of the number of real roots for coefficients with a nonzero mean value mu_n = E(c_i) scaled as mu_nsim n^{-1/2}." @default.
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- W2097079886 date "2004-01-09" @default.
- W2097079886 modified "2023-09-24" @default.
- W2097079886 title "Real roots of random polynomials: universality close to accumulation points" @default.
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- W2097079886 doi "https://doi.org/10.1088/0305-4470/37/4/011" @default.
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