Copolymers at selective interfaces: settled issues and open problems

TL;DR

This paper reviews the current understanding of copolymer localization at selective interfaces, summarizes key results, discusses proof techniques, and highlights unresolved questions in the field.

Contribution

It provides a comprehensive review of existing results, offers simplified alternative proofs, and identifies open problems in copolymer interface localization research.

Findings

Summarizes key results on copolymer localization transition.

Provides simplified proofs for existing results.

Highlights open problems and future research directions.

Abstract

We review the literature on the localization transition for the class of polymers with random potentials that goes under the name of copolymers near selective interfaces. We outline the results, sketch some of the proofs and point out the open problems in the field. We also present in detail some alternative proofs that simplify what one can find in the literature.