Can I calculate limiting distributions?

Yes, the skill includes functions to verify Tracy-Widom GUE limits for passage times in large systems and rescales models toward the Directed Landscape.

Which weight distributions does this skill support?

It supports Exponential, Geometric, Bernoulli, and Inverse-Gamma distributions for grid weights, allowing for a variety of limit behavior studies.

How does this skill relate to TASEP?

LPP passage times are mathematically equivalent to the integrated current in the Totally Asymmetric Simple Exclusion Process (TASEP), and geodesics correspond to second-class particle trajectories.

What is Last Passage Percolation (LPP)?

LPP is a stochastic model where the goal is to find the path through a grid that maximizes the sum of random weights, serving as a discrete version of the KPZ growth model.

Last Passage Percolation Modeling

Name: Last Passage Percolation Modeling
Author: plurigrid

byplurigrid

•

Data Science & ML

Simulates and analyzes Last Passage Percolation models to study Tracy-Widom fluctuations, geodesics, and KPZ universality.

This skill provides a comprehensive suite of tools for investigating Last Passage Percolation (LPP), a fundamental discrete model in the Kardar-Parisi-Zhang (KPZ) universality class. It enables users to compute passage times across various weight distributions including Exponential, Geometric, and Bernoulli, while visualizing optimal paths and analyzing competition interfaces. By integrating advanced concepts like the Robinson-Schensted-Knuth (RSK) correspondence and the Matrix Product Ansatz, it facilitates deep exploration of the connections between stochastic particle systems like TASEP and random matrix theory, making it an essential utility for researchers in statistical mechanics and probability.

Key Features

018 GitHub stars

02Efficient computation of maximum weight paths and passage times via dynamic programming

03Simulation of LPP models with multiple weight distributions including Exponential and Geometric

04RSK correspondence implementation linking LPP to Young tableaux and random matrices

05Geodesic backtracking and competition interface analysis for path optimality

06Integration with TASEP and KPZ universality scaling limits for comprehensive system modeling

Use Cases

01Analyzing stochastic growth models and fluctuations in 2D discrete grids

02Verifying Tracy-Widom limiting distributions for large-scale random matrix systems

03Mapping particle dynamics in TASEP to discrete percolation paths for current analysis

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi last-passage-percolation

For use in Claude.ai and ChatGPT

Download Skill