Chaining, interpolation, and convexity

Seminar | October 4 | 3:10-4 p.m. | 1011 Evans Hall

 Ramon van Handel, Princeton University

 Department of Statistics

Classical estimates on the suprema of random processes in terms of metric
entropy have found widespread use in probability theory, statistics,
computer science, and other areas. Such estimates are powerful and easy to
use, but often fail to be sharp. To obtain sharp bounds, one must replace
these methods by a multiscale analogue known as the generic chaining that
was developed by Talagrand. Unfortunately, the latter is notoriously
difficult to use in any given situation. In this talk, I will exhibit a
surprisingly simple construction, inspired by real interpolation of Banach
spaces, that is readily amenable to explicit computations. Despite its
simplicity, the method proves to be sufficiently powerful to recover the
central results in Talagrand's theory in a very simple way. The talk will
focus on some basic ideas and will be illustrated by specific examples; I
will not assume prior familiarity with the topic. If time permits, I will
briefly outline applications to the majorizing measure theorem and randommatrices, as well as some embarrassing open problems.