What is the primary purpose of this skill?

It provides the specialized capabilities needed to model and analyze the stationary measures of the Kardar-Parisi-Zhang (KPZ) equation using Liouville quantum gravity principles.

How does it handle the mathematical roughness of the KPZ equation?

The skill utilizes increments and derivative measures where distributions are well-defined, applying Liouville measures and Gaussian Free Field corrections to ensure analytical rigor.

Does it support specific boundary conditions?

Yes, it specifically handles open boundary conditions defined by U and V slope parameters, including the generation of phase diagrams for low/high density and maximal current phases.

Can this skill be used for discrete probability models?

Yes, it includes integration for Geometric Last Passage Percolation (LPP) to replicate KPZ stationary structures in discrete grid settings.

Louisville Quantum Gravity

Name: Louisville Quantum Gravity
Author: plurigrid

byplurigrid

•

Data Science & ML

Analyzes and implements stationary measures for the KPZ equation using Liouville quantum gravity and matrix product ansatz.

The Louisville Quantum Gravity skill provides specialized mathematical and physical domain knowledge for studying the Kardar-Parisi-Zhang (KPZ) equation. It enables Claude to model time-invariant distributions, navigate complex phase diagrams for open boundary conditions, and apply two-layer Gibbs measures. This skill is essential for researchers and developers working on stochastic growth models, random geometry, and infinite-dimensional analytic continuation where traditional differentiability fails and measure-theoretic approaches are required.

Key Features

01Calculates phase diagrams based on boundary slope parameters (U, V)

02Facilitates analytic continuation from finite to infinite-dimensional spaces

038 GitHub stars

04Implements Gaussian Free Field (GFF) sampling for LQG area measures

05Models stationary measures for KPZ equations with open boundary conditions

06Provides Matrix Product Ansatz structures for stationary weight calculations

Use Cases

01Simulating stochastic surface growth and interface roughness in theoretical physics

02Analyzing long-time limits and phase transitions in open boundary systems

03Verifying measure-theoretic consistency in infinite-dimensional probability models

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi louisville-quantum-gravity

For use in Claude.ai and ChatGPT

Download Skill