Armen Vagharshakyan Discrepancy and the Small Ball Inequality

S EMINARIO
DE
A N ÁLISIS
Departamento de Matemáticas. Universidad Autónoma de Madrid
Viernes, 3 de abril de 2009
11:00 h. en el aula C-XV-520
Armen Vagharshakyan
Georgia Institute of Technology
Discrepancy and the Small Ball
Inequality
Resumen: The Small Ball Inequality refers to the lower bound for the L∞ norm
of linear combinations of multidimensional Haar functions adapted to rectangles of a fixed volume. We obtain the first non-trivial improvement over the
average case bound in dimensions four and higher. The relevant results are
known in dimension 2, a result due to W. Schmidt and M. Talagrand, with important contributions from Halasz and Temlyakov. J. Beck established a prior
result in dimension 3, whose argument we extend. The relation of these results
to the Discrepancy theory is also outlined.
This is joint work with Dmitriy Bilyk and Michael Lacey.