An elementary proof of the majorizing measure theorem

Tuesday, January 31, 2017 - 2:00pm
Math Sci 111
Ramon van Handel

The majorizing measure theorem of Talagrand provides a sharp description
of the expected supremum of any Gaussian process in terms of the geometry
of its index set. It plays a fundamental role in various problems in
probability theory and functional analysis. However, this deep result has
the reputation of being notoriously delicate and difficult to use. In this
talk, I will show a new proof of the majorizing measure theorem that is
completely elementary. More importantly, the two basic ingredients on
which this proof is based--a simple contraction principle and an
interpolation method--provide a powerful mechanism for bounding the
suprema of Gaussian processes in concrete situations. If time permits, I
will sketch an application to the norms of inhomogeneous random matrices.

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