README.md

Tensor $z$-eigenvalues

Code that quickly generates $z$-eigenvalues of a tensor. For a 3 dimensional tensor, $C_{i,j,k}$, a $z$-eigenpair, $(x_i, \lambda)$ satisfies $C_{i, j, k} x_i x_j = \lambda x_k$. The eigenvalues correspond to the energy of a spherical $p$-spin model. This code solves for every eigenpair of a $N$ dimensional tensor with the tensor being generated for various ensembles of tensors.

Folder Structure

• analysis/
  • Python scripts to calculate statistics from datasets of $z$-eigenvalues.
• energyLandscape/
  • Code to visualize the energy landscape of a low dimensional spherical $p$-spin model.
• gumbelTheory/
  • Known statistics about the spherical $p$-spin model.
• mathematicaMonteCarlo/
  • Mathematica notebooks to generate $z$-eigenvalues for tensors of different ensembles.
• metropolisEnsemble/
  • Matlab code which uses the Wang-Landau algorithm to estimate the distribution of the maximum $z$-eigenvalue. This algorithm is much quicker to explore the tails of the distribution compared to random sampling.
• samplingEigenValues/
  • Matlab code to generate $z$-eigenvalues for tensors of different ensembles. Bash scripts to run using SLURM on a HPC.