Skip to main content
Browse by:

Effective March 10, 2020, all Duke-sponsored events over 50 people have been cancelled, rescheduled, postponed or virtualized.
Please check with the event contact regarding event status. For more information, please see

Real roots of random functions

Event Image
Icon calendar
Monday, December 16, 2019
Icon time
12:15 pm - 1:15 pm
Icon speaker
Oanh Nguyen (Princeton University)
Icon series
Probability Seminar

Random functions are linear combinations of deterministic functions using independent random coefficients. These innocent-looking objects appear naturally in physics and approximation theory and remain mysterious despite decades of intensive research. We will discuss recent progress on the study of random functions and present our approach via the local universality method to study questions on the real roots. Among the applications, we derive a sharp bound on the mean number of real roots for the Kac polynomial which confirms a conjecture by Kac in 1943. We will also discuss the mean, variance, and the limiting distribution of the number of real roots for several classes of random functions. This talk is based on several joint papers with Mei-Chu Chang, Yen Do, Hoi Nguyen, and Van Vu.