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Non-Backtracking theory
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Classroom Contents
Weingarten Calculus and Its Applications
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- 1 Intro
- 2 Contents
- 3 The Haar measure on compact groups
- 4 Polynomial functions on a matrix group
- 5 Fundamental integration formula
- 6 Historical remarks and comments
- 7 Representation theoretic formulas (unitary case)
- 8 Combinatorial formulations
- 9 Digression: the quantum group case
- 10 Leading order Asymptotics of Wg (U, case)
- 11 Applications of the asymptotics (a subjective selection)
- 12 Asymptotic freeness (pointwise, leading order)
- 13 Asymptotic freeness: quantum (pointwise, leading order)
- 14 Quantum Information (pointwise, leading order)
- 15 Higher order asymptotic freeness (higher order)
- 16 Matrix integrals and random tensors (higher order)
- 17 Uniform estimates
- 18 Centered version
- 19 Strong Asymptotic freeness Centering
- 20 Outline of the proof
- 21 Non-Backtracking theory
- 22 Concluding remarks
