An upper bound on the smallest singular value of a square random matrix

Series
Analysis Seminar
Time
Wednesday, April 11, 2018 - 1:55pm for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Kateryna Tatarko – University of Alberta – tatarko@ualberta.ca – https://www.msri.org/people/39313
Organizer
Galyna Livshyts
Consider an n by n square matrix with i.i.d. zero mean unit variance entries. Rudelson and Vershynin showed that its smallest singular value is bounded from above by 1/sqrt{n} with high probability, under the assumption of the bounded fourth moment of the entries. We remove the assumption of the bounded fourth moment, thereby extending the result of Rudelson and Vershynin to a wide range of distributions.