OAI/GroupTheory/PolycyclicRecognition/Algebra/RegularWalkEnergyLowerBound.lean

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3 declarations, 0 contain sorry, 0 declared as axioms

Polynomial lower bounds for regular random-walk energy

The probability mass is supported on one word ball. An adjacent larger ball contains a point where the vector vanishes. The cocycle word estimate then gives a quantitative lower bound for its generator energy.

  1. theorem OAI.PolycyclicRecognition.regularHilbert_point_difference_bound line 17
  2. theorem OAI.PolycyclicRecognition.regularProbability_energy_lower line 39
  3. theorem OAI.PolycyclicRecognition.regularLazyWalk_polynomial_energy_lower line 78