# Stochastic Renormalization Group and Gradient Flow

## TL;DR

This paper introduces a stochastic approach to renormalization group transformations inspired by Fokker-Planck equations, enabling lattice simulations and linking long-distance correlations to gradient flow, with implications for measuring anomalous dimensions.

## Contribution

It proposes a non-perturbative, stochastic RG framework based on Fokker-Planck equations, facilitating lattice simulations and analysis of correlations via gradient flow.

## Key findings

- Effective Boltzmann factors follow Fokker-Planck equations.
- Long-distance correlations approach gradient-flowed correlations.
- RG scaling formula enables measurement of anomalous dimensions.

## Abstract

A non-perturbative and continuous definition of RG transformations as stochastic processes is proposed, inspired by the observation that the functional RG equations for effective Boltzmann factors may be interpreted as Fokker-Planck equations. The result implies a new approach to Monte Carlo RG that is amenable to lattice simulation. Long-distance correlations of the effective theory are shown to approach gradient-flowed correlations, which are simpler to measure. The Markov property of the stochastic RG transformation implies an RG scaling formula which allows for the measurement of anomalous dimensions when transcribed into gradient flow expectation values.