Dear all,
I would like to announce the following online seminar
that will take place next week via the Zoom platform.
Best regards, Maurizia Rossi
Tuesday, Jan 19 - 4:30pm (Rome time zone)
Speaker: Arturo Jaramillo Gil (CIMAT -
Centro de Investigación en matemáticas, Mexico)
Title: Quantitative Erdös-Kac theorem for additive functions
Summary:
The
talk will take as a starting point the celebrated Erdös-Kac theorem; a
result of great importance in probabilistic number theory, which
establishes that the fluctuations of the number of prime factors in a
uniform sample over {1,..., n} are asymptotically Gaussian. Naturally,
after the publication of this result, many quantitative versions of it
have been studied. LeVeque conjectured that the optimal rate was
asymptotically equivalent to loglog(n)^(-1/2). This was later proved by
Turan and Rényi by means of an ingenious manipulation of the underlying
characteristic function. Unfortunately, up to this day, all the
perspectives for solving LeVeque's conjecture are based on the use of
non-trivial complex analysis tools, while the probabilistic perspective
has been only successfully applied to obtain suboptimal rates of
convergence. In this talk, we will give a purely probabilistic proof of
LeVeque's conjecture which will allow us to address the problem in a
general fashion by means of Stein's method techniques.
Link Zoom
https://us02web.zoom.us/j/88100676046?pwd=NTFjdlAyVjdSTE8rVnBmUGVWelFPdz09
Meeting ID: 881 0067 6046
Passcode: 680246