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On the Distribution of Critical Points of a Polynomial
Critical Points Polynomial Probability
2012/7/11
This paper proves that if points $Z_1,Z_2,...$ are chosen independently and identically using some measure $\mu$ from the unit circle in the complex plane, with $p_n(z) = (z-Z_1)(z-Z_2)...(z-Z_n)$, th...
Distance Functions, Critical Points, and Topology for Some Random Complexes
Distance function critical points Morse index Cech complex Poisson process central limit theorem Betti numbers
2011/9/20
Abstract: For a finite set of points $P$ in $R^d$, the function $d_P:R^d \to R_+$ measures Euclidean distance to the set $P$. We study the number of critical points of $d_P$ when $P$ is random. In par...