Even-Exponent Dihedral Monotonicity

This is a Lean formalization of the monotonicity of even-exponent distances for continuous-time random walks on dihedral groups.

Main Results

• For every n ≥ 2 and every m ≥ 1, raising the jump rates of a symmetric walk on the dihedral group D_n cannot increase the ℓ^{2m} distance of its time-t distribution from uniform.

See §Formal Challenge for a formal certificate.

Dependencies

This depends on Mathlib.

Formal Challenge

A formal challenge file certifying that this repository does formalize the results claimed above is located at Challenge/Basic.lean. This file only depends on the dependency above. It contains formal statements of §Main Results with sorry as proof.

This repository can be verified against the formal challenge with the Lean comparator on a Linux machine. First, follow the instructions in https://github.com/leanprover/comparator to install comparator. Then, run the following command:

lake env comparator Comparator/comparator.json

This repository has been locally verified with the comparator.