Measure concentration for vector valued functions on Hamming cube

TL;DR

This paper establishes a measure concentration inequality for Lipschitz functions mapping the Hamming cube into Banach spaces with finite cotype, extending the understanding of concentration phenomena in high-dimensional discrete structures.

Contribution

It introduces a new concentration inequality for vector-valued functions on the Hamming cube, applicable to Banach spaces of finite cotype, broadening previous scalar results.

Findings

Proves measure concentration for vector-valued functions on the Hamming cube.

Extends concentration inequalities to Banach spaces of finite cotype.

Provides tools for analyzing high-dimensional discrete structures with vector outputs.

Abstract

We prove here the concentration of measure inequality for Lipschitz function on the Hamming cube with values in any Banach spaces of finite cotype.