Large deviations for lacunary trigonometric sums
Kavita Ramanan, Roland George Dwight Richardson University Professor of Applied Mathematics - Brown University
Lacunary trigonometric sums are known to exhibit several properties that are typical of sums of iid random variables such as the central limit theorem, established by Salem and Zygmund, and the law of the iterated logarithm, due to Erdos and Gal. We initiate an investigation of large deviation principles for such sums, and show that they display several interesting features, including sensitivity to the arithmetic properties of the corresponding lacunary sequence. This is joint work with C. Aistleitner, N. Gantert, Z. Kabluchko and J. Prochno.