Analysis called Hypercontractivity. We shall see the theorem and a few of its ... Hypercontractivity. Even the q-th norm of Tρ(f ) is smaller than the p-th ...

The notion of hypercontractivity first arose in quantum field theory [3] and underwent much development in functional analysis and mathematical physics.

The hypercontractivity theorem says that Tρ is actually a hypercontractive map, in that it smooths out f even when one measures Tρf in a higher norm. With ...

Feb 15, 2010 · Hypercontractive inequalities are a useful tool in dealing with extremal questions in the geometry of high-dimensional discrete and continuous ...

Mar 8, 2007 · The idea behind the statement is that the Tρ operator smooths, or “reasonable-izes”, functions. Theorem 1.1 (Hypercontractivity Theorem.) ...

Jan 31, 2023 · In this lecture, we overview the theory of hypercontractivity and its applications to understand- ing expansion of higher order random walks ...

For the past twenty years, a set of ideas known as hypercontractivity has played a continuing role in analysis with ramifications in quantum field theory, self- ...

Nov 17, 2021 · In this work, we develop a new theory of hypercontractivity on high dimensional expanders (HDX), an important class of expanding complexes that ...

The hypercontractivity theorem gives the reverse inequality when we add some noise. ... The hypercontrac- tive inequality controls the relation between the two.

The hypercontractivity theorem says that Tρ is actually a hypercontractive map, in that it smooths out f even when one measures Tρf in a higher norm. With ...