September

October

Krzysztof Oleszkiewicz (University Warsaw): On the asymptotics of the optimal constants in the Khinchine-Kahane inequality

Let us consider a sequence of indepenedent symmetric +/-1 random variables, often called the Rademacher system. A linear combination of these random variables is a real random variable called a (weighted) Rademacher sum. There are also vector-valued Rademacher sums, in which the real coefficients in the linear combination are replaced by vectors from some normed linear space. Rademacher sums, both real and vector-valued, have been studied for more than 100 years now. In the talk, classical moment inequalities for Rademacher sums will be described, going back to Khinchine (1923) and Kahane (1964), as well as some more recent results.

Devraj Duggal (University of Minnesota): On Spherical Covariance Representations

We first motivate the study of covariance representations by surveying preceding results in the Gaussian space. Their spherical counterparts are then derived thereby allowing applications to the spherical concentration phenomenon. The applications include second order concentration inequalities. The talk is based on joint work with Sergey Bobkov.

(No recording available)

Rafał Latała (University of Warsaw): On the spectral norm of Rademacher matrices

We will discuss two-sided non-asymptotic bounds for the mean spectral norm of nonhomogenous weighted Rademacher matrices. We will present a lower bound and show that it may be reversed up to log log log n factor for arbitrary n×n Rademacher matrices. Moreover, the triple logarithm may be eliminated for matrices with 0,1-coefficients.

(No recording available)

Miquel Saucedo (Universitat Autònoma de Barcelona): Weighted inequalities for the Fourier transform

In this talk we discuss inequalities for the Fourier transform between weighted Lebesgue spaces and their connection with an interpolation technique due to Calderón.

(Pending permission to publish the recording)

Guy Kindler (The Hebrew University of Jerusalem): Bounded functions with small tails are Juntas

There seems to be some recent interest in structural results concerning functions whose Fourier transform is mostly supported on `low-degrees'  while their range is restricted to a specific set. This is at least partly motivated by applications to Theoretical Computer Science. In this talk I will go over a not-so-recent result with this theme, which shows that a function f over the discrete hypercube whose Fourier representation is `mostly' of low degree and which obtains values in the (continuous) segment [-1,1] must be close to a junta, namely it can be approximated by only looking at a constant number of input-coordinates. The proof goes by showing a large-deviation lower bound for low degree functions that uses some tricks that may be of interest. If time permits I may also talk about some improvements to our result made by O’Donnell and Zhao. Joint work with Irit Dinur, Ehud Friedgut, and Ryan O'Donnell.

(No recording available)