4 problems

Non-universality conjecture for the first non-universal term in Kac polynomial real zeros
Let $P_n(x)=\sum_{k=0}^{n}\xi_kx^k$ be a Kac random polynomial, where the coefficients $\xi_k$ are independent and identically distributed copies of a random variable $\xi$ . Assume…
openFrom papersprobability random-polynomials real-roots
0 responses
10
Polynomial concentration conjecture for the number of real zeros of Kac polynomials
Concentration conjecture. Under mild conditions, the probability that the number of real zeros deviates from its expectation by at least $\varepsilon\log n$ is bounded above and be…
openFrom papersconcentration-inequalities random-polynomials real-roots
0 responses
7
O. Nguyen's intermediate real-root count conjecture for random polynomials
O. Nguyen's conjecture. Given $\alpha\in(0,1)$ , there exists a bounded sequence $(c_k)$ of real numbers such that
openFrom papersprobability random-polynomials real-roots
0 responses
11
Distinct positive zeros of the derivative-polynomial combinations
Polynomial distinct-zeros conjecture. The positive real zeros of the polynomials
openFrom paperselectrical-fields polynomials real-roots
0 responses
3

Non-universality conjecture for the first non-universal term in Kac polynomial real zeros