# Sub-ballisticity of self-repelling polymers in Z^d

## TL;DR

This paper proves that self-repelling polymers in Z^d exhibit sub-ballistic behavior, extending previous results from self-avoiding walks to a broader class with more flexible self-intersection penalties.

## Contribution

It establishes sub-ballisticity for a general class of self-repelling polymers with arbitrary step distributions and flexible intersection penalties, broadening understanding beyond self-avoiding walks.

## Key findings

- Self-repelling polymers are sub-ballistic in Z^d.
- The result generalizes previous work on self-avoiding walks.
- Flexible intersection penalties still lead to sub-ballistic behavior.

## Abstract

In this article, we prove sub-ballisticity for a class of self-repelling polymers inZ^d. Self-repelling polymers are a two-way generalization of the model of self-avoiding walks, for which the sub-ballisticity was proved by H. Duminil-Copin and A. Hammond. Namely, we consider an arbitrary finite symmetric distribution of steps and a more flexible penalization for self-intersections than in the self-avoiding walks model.