16 citations · 27 across the 24 of their papers we have counts for
4 papers · 1 filter
Sums of random polynomials with differing degrees
Isabelle Kraus, Marcus Michelen, Sean O'Rourke
Let and be probability measures in the complex plane, and let and be independent random polynomials of degree , whose roots are chosen independently from and…
Direct design of biquad filter cascades with deep learning by sampling random polynomials
Joseph T. Colonel, Christian J. Steinmetz, Marcus Michelen +1
Designing infinite impulse response filters to match an arbitrary magnitude response requires specialized techniques. Methods like modified Yule-Walker are relatively efficient, bu…
The singularity probability of a random symmetric matrix is exponentially small
Marcelo Campos, Matthew Jenssen, Marcus Michelen +1
Let be drawn uniformly at random from the set of all symmetric matrices with entries in . We show that \[ \mathbb{P}( \det(A) = 0 ) \leq e^{-cn},\] where…
Anti-concentration of random variables from zero-free regions
Marcus Michelen, Julian Sahasrabudhe
This paper provides a connection between the concentration of a random variable and the distribution of the roots of its probability generating function. Let be a random variab…