# A higher Boltzmann distribution

@article{Catanzaro2017AHB,
title={A higher Boltzmann distribution},
author={Michael J. Catanzaro and V. Chernyak and J. R. Klein},
journal={Journal of Applied and Computational Topology},
year={2017},
volume={1},
pages={215-240}
}
• Published 2017
• Mathematics, Computer Science, Physics
• Journal of Applied and Computational Topology
AbstractWe characterize the classical Boltzmann distribution as the unique solution to a combinatorial Hodge theory problem in homological degree zero on a finite graph. By substituting for the graph a CW complex X and a choice of degree $$d \le \dim X$$d≤dimX, we define by direct analogy a higher dimensional Boltzmann distribution $$\rho ^B$$ρB as a certain real-valued cellular $$(d-1)$$(d-1)-cycle. We then give an explicit formula for $$\rho ^B$$ρB. We explain how these ideas relate to the… Expand
8 Citations

#### References

SHOWING 1-10 OF 25 REFERENCES
Simplicial complexes: Spectrum, homology and random walks
• Mathematics, Computer Science
• Random Struct. Algorithms
• 2017
• 54
• PDF
Simplicial and Cellular Trees
• Mathematics
• 2016
• 19
• PDF
Cellular spanning trees and Laplacians of cubical complexes
• Mathematics, Computer Science