# Real-Space Renormalization for disordered systems at the level of Large Deviations

## TL;DR

This paper investigates how real-space renormalization affects the large deviation tails of probability distributions in disordered systems, specifically analyzing the directed polymer model to understand tail behaviors and rate functions.

## Contribution

It introduces a method to analyze the renormalization flows of distribution tails, extending beyond typical fluctuations to large deviations in disordered systems.

## Key findings

- Renormalization flows for distribution tails can be characterized in the directed polymer model.
- The tail behaviors of the initial conditions influence the renormalization flow outcomes.
- The study provides insights into the scaling of large deviations in disordered media.

## Abstract

The real-space renormalization procedures on hierarchical lattices have been much studied for many disordered systems in the past at the level of their typical fluctuations. In the present paper, the goal is to analyze instead the renormalization flows for the tails of probability distributions in order to extract the scalings of their large deviations and the tails behaviors of the corresponding rate functions. We focus on the renormalization rule for the ground-state energy of the Directed Polymer model in a random medium, and study the various renormalization flows that can emerge for the tails as a function of the tails of the initial condition.