# Random paths with curvature

## TL;DR

This paper investigates a Monte Carlo simulation of curved random paths, exploring their transition from flexible to rigid states and drawing parallels with crumpling transitions in random surface theories.

## Contribution

It introduces a curvature-dependent action model for random paths and analyzes the transition behavior, providing insights into the physics of random surfaces.

## Key findings

- Identified a transition from free to rigid paths.
- Draws parallels with crumpling transitions.
- Provides a toy model for random surface theory.

## Abstract

We present some results coming from a Monte Carlo simulation of a set of random paths with a curvature dependent action. This model can be considered as a toy model of the theory of random surfaces. The transition from free to rigid random paths has been analyzed and the similitude with the crumpling transition have been pointed out.