Probability and Mathematical Physics Seminar

Convergent points for random power series on the unit circle

Time and Location:

Oct. 31, 2025 at 11:10AM; Warren Weaver Hall, Room 1302

Speaker:

Mehtaab Sawhney, Columbia University

Link:

Seminar homepage

Abstract:

Consider a random power series P(z) = \sum a_n\epsilon_nz^{n} where \epsilon_n\in \{+-1\} uniformly at random. We prove that if a_n = o(1/\sqrt{n}) then there exists a Hausdorff dimension 1 set on |z| = 1 such that P(z) is a convergent sum. This answers, in a strong form, a conjecture of Erdos.
Joint w. Marcus Michelen