Category: Statistics

Summary: Estimating the fluctuation exponent for two-dimensional first-passage percolation and testing the KPZ prediction across several edge-weight distributions.

First-passage percolation assigns random travel times to edges of a lattice and asks how the minimum travel time grows and fluctuates with distance. This experiment focuses on the fluctuation exponent chi in two dimensions, which KPZ theory predicts should equal one third even though rigorous bounds remain much weaker.

The simulation runs Dijkstra searches on square lattices with exponential, uniform, and gamma edge weights. By measuring the variance of passage times at increasing distances and fitting the resulting scaling law, it estimates the exponent and checks whether the same value appears across different distribution families.

That comparison matters because most prior numerical evidence has been limited in scale or distribution coverage. The experiment is designed to build a broader finite-size estimate of a central KPZ-universality quantity rather than relying on a single weight law or small-lattice study.

Method: Repeated Dijkstra computations on 2D lattices with log-log scaling fits of passage-time variance to estimate the fluctuation exponent chi.

What is measured: Passage-time variance, estimated fluctuation exponent chi, fit quality, and comparisons across exponential, uniform, and gamma edge weights.