1
Spectral theory of regular graphs
▶
1.1
Basic notions of graph theory
▶
1.1.1
General definitions
1.1.2
Paths and distance
1.1.3
Notions of finiteness
1.1.4
Degree and regularity
1.2
Adjacency operator
▶
1.2.1
Constant fonctions
1.2.2
Definition of the adjacency operator and elementary properties
1.2.3
Norm of the adjacency operator
1.2.4
Adjacency operator is self-adjoint
1.2.5
The case of regular graphs
1.2.6
The case of finite graphs
1.2.7
The case of finite regular graphs
2
Analytic tools
▶
2.1
Spaces of functions and norms
2.2
Markov inequalities
2.3
Chebyshev polynomials
2.4
Compactly supported distributions
Dependency graph
Friedman’s theorem: a new proof using strong convergence
Laura Monk
1
Spectral theory of regular graphs
1.1
Basic notions of graph theory
1.1.1
General definitions
1.1.2
Paths and distance
1.1.3
Notions of finiteness
1.1.4
Degree and regularity
1.2
Adjacency operator
1.2.1
Constant fonctions
1.2.2
Definition of the adjacency operator and elementary properties
1.2.3
Norm of the adjacency operator
1.2.4
Adjacency operator is self-adjoint
1.2.5
The case of regular graphs
1.2.6
The case of finite graphs
1.2.7
The case of finite regular graphs
2
Analytic tools
2.1
Spaces of functions and norms
2.2
Markov inequalities
2.3
Chebyshev polynomials
2.4
Compactly supported distributions