Category: Statistics

Summary: Comparing how quickly different edge-weight distributions approach the KPZ wandering exponent prediction in two-dimensional first-passage percolation.

First-passage percolation is a central model for random growth and disordered transport, and in two dimensions it is expected to fall into the KPZ universality class. This experiment asks not only whether the wandering exponent approaches the predicted value of one third, but whether different edge-weight distributions approach that limit at different rates.

The script assigns random non-negative weights to lattice edges, computes minimum-weight paths across multiple system sizes, and estimates effective exponents for exponential, uniform, mixed discrete-continuous, and gamma-distributed disorder. The focus is on finite-size convergence, not just the putative asymptotic value.

That is useful because many numerical studies emphasize a single disorder family. Here the comparison across several distributions probes whether subleading corrections and approach-to-scaling behavior are themselves structured and distribution dependent.

Method: Repeated first-passage percolation simulations on the two-dimensional square lattice, with shortest-path solves and finite-size exponent estimation across several weight distributions.

What is measured: Effective wandering exponent by scale, passage-time fluctuation scaling, dependence on edge-weight distribution, and convergence toward the KPZ prediction.