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math.PR2021★ 1 cited
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…
math.PR2021
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…