probability-statistics / Random Polynomials
For $P_n(z) = \sum_{k=0}^n \varepsilon_k z^k$ with independent uniform signs, does the number $R_n$ of roots in $|z| \le 1$ satisfy $R_n/(n/2) \to 1$ almost surely? The manuscript proves the strong law with $R_n = n/2 + O_\omega(n^{149/150})$.
Temporal state
No reconciled state yet.
Append-only history
For $P_n(z) = \sum_{k=0}^n \varepsilon_k z^k$ with independent uniform signs, does the number $R_n$ of roots in $|z| \le 1$ satisfy $R_n/(n/2) \to 1$ almost surely? The manuscript proves the strong law with $R_n = n/2 + O_\omega(n^{149/150})$.
Research memory
For $P_n(z) = \sum_{k=0}^n \varepsilon_k z^k$ with independent uniform signs, does the number $R_n$ of roots in $|z| \le 1$ satisfy $R_n/(n/2) \to 1$ almost surely? The manuscript proves the strong law with $R_n = n/2 + O_\omega(n^{149/150})$.
Evidence graph
No public relationships recorded yet.