Events

COSAM Events 2014 March Stochastics Seminar

Stochastics Seminar

Time: Mar 19, 2014 (04:00 PM)
Location: Parker Hall 224

Details:
Speaker: Dr. Jerzy Szulga
 
Title: Paley-Marcinkiewicz-Zygmund property and its consequences
 
Abstract:
In 1930’s Paley and Zygmund became interested in random Fourier series , where was a sequence of i.i.d. random variables, most notably Rademacher (random signs), or Steinhaus (uniform on the unit circle), or Gaussian. Such series can be viewed as random series with coefficients from a Banach space (of continuous functions, , Orlicz, etc.). The striking 1920’s Khinchin’s inequality for real Rademacher series
has been extended to Banach space valued coefficients and the best constant has been found. In 1930s Marcinkiewicz and Zygmund analyzed a similar “reversal” of Jensen’s inequality for sums of independent random variables, and in 1960s Rudin investigated a similar property for portions of Walsh series (Walsh functions are characters of the dyadic group and can be seen as products of Rademacher functions).
 
The seminar talk will describe the nexus of such “inverse” phenomena, e.g., classical inequalities and relations valid in inverse, contraction without convexity, hypercontraction (to be explained), etc., with potential application to statistics, harmonic analysis,  random chaos, and all kinds of things stochastic.