Student Probability Seminar

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Limit Theorems for Empirical Density of Greatest Common Divisors

Speaker: Behzad Mehrdad

Location: Warren Weaver Hall 905

Date: Tuesday, November 5, 2013, 3:30 p.m.

Synopsis:

The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical density. We will also obtain a sharp rate of convergence to the normal distribution for the central limit theorem. Some generalizations are provided. this is joint work with Lingjiong Zhu.