 -trace 17 36
Abelian covering manifold 14
Absolutely continuous coupling constants 5
Absolutely continuous IDS 36
Absolutely continuous spectrum 7—9
Admissible exhaustion 19
Aizenman — Molchanov technique see "Fractional moment method"
Alloy type, model 3 5 8 34
Alloy type, potential 5 7
Amenable group 17 20 29
Anderson localisation 7 37
Anderson model 33 35 64
b.c. see "Boundary conditions"
Bernoulli distributed coupling constants 35
Bernoulli distribution 35
Bernoulli — Anderson potential 3
Bernoulli, disorder 40
Bernoulli, random variables 3
Bethe — Sommerfeld conjecture 12
Betti number 36
Binary alloy 3
Bishop's theorem see "Volume comparison theorem"
Bound state 7
boundary conditions 4 14 33
Boundary conditions, independence 33
Boundary tube 19
Bounded random operator 16
Brownian motion 24
Common density 63 65
Conditional densities of coupling constants 65
Contraction, semigroup 24
Convolution vector 62
Correlated coupling constants 65
Coupling constants 5
Decay of eigenfunctions 7—8
Decay of Green function 39
Decay of heat kernel 23
Delocalised states 8
Density of states 33 35 57
Density of states, measure 10
Dirichlet form 24
Dirichlet — Neumann bracketing 11 31 53 58 66
Discontinuous IDS 36
Distribution function 10—11 17 29
Distribution of coupling constant 5
Distribution of eigenvalues 37
Distribution of potential values 35
Domain monotonicity 25
DOS see "Density of states"
Doubling property see "Tempelman property"
Dynamical localisation 8
Effective Hamiltonian on a manifold 11
Equivariance 14
Ergodic 3
Ergodic action 5
Ergodic operator 6
Ergodic potential 6
Ergodic theorem 11 29 31
Exhaustion 18 19
Exponential localisation 7
Extended state see "Scattering state"
Extension operator 69 70
Extension property 33
Extra-potential 11
Feynman — Kac formula 24
Finite dimensional distributions 6
Finite volume integrated density of states see "Normalised eigenvalue counting function"
Fluctuation boundaries of the spectrum 9
Foelner sequence 18
Fractional moment method 38
Friedrichs extension 14
Fundamental domain 14
Fundamental solution of heat equation 25
Generalised step function 62
Gronwall's lemma 52
Heat equation 26
Heat equation, kernel 23 25
Heat semigroup 28
Heisenberg group 15
Hellmann — Feynman formula 44 49 52
Hilbert — Schmidt class 8 69
Hoelder continuity of coupling constants 54
Hoelder continuity of IDS 35 46 53
Hoelder continuous coupling constants 54
Holomorphic family of operators 44
Hyperbolic space 19
IDS see "Integrated density of states"
Infinitesimally bounded 5 57
Initial scale estimate 38 39
Integrated density of states 10 20
Interlacing theorem 53
| Kato — Rellich theorem 5
Kato — Simon inequality 70
Kernel of semigroup 66
Krein trace formula 67
Laplace transform 10 30
Laplace — Beltrami operator 12 13 36
Level statistics 37
Lifshitz tails 9 33
Lipschitz continuity 35 51 56
Localisation, interval 7
Locally continuous coupling constants 49
Log-Hoelder continuity 36
Long range correlations 7
Long range single site potentials 55
Magnetic potential 53 66 70
Markov, semigroup 24
Maximum principle 26
Measurability 20
Measurable family of operators 20
Measure preserving transformations 6
Mobility edge 8 33
Multiscale analysis 35 55
Non-randomness of spectra 16
Normalised eigenvalue counting function 10
Off-diagonal decay of heat equation, kernel 23
One-electron Hamiltonian 2
Operator domain 4
Pastur — Subin convergence criterion 30
Pastur — Subin trace formula 10 20
Percolation 36
Periodic operator on manifold 12 20
Periodic potential 9
Points of increase 17
Pointwise ergodic 18
Polyhedral domain 14
Positivity preserving semigroup 24
Principle of not feeling the boundary 23
Pure point spectrum 7 37
Quadratic form 14 22
Quadratic form, domain 22
Quantum percolation model 36
Quantum waveguides 12
Quasi-norm 68
Random metric 13
Random Schroedinger operator 2 14
Relative form-boundedness 5
Relatively bounded 4
Resonance 40 41
Ricci curvature 13
Scattering state 7
Schroedinger equation 7
Schroedinger operator on manifold 11
Schroedinger, semigroup 47
Self-averaging 10
Semigroup 23 24 26 30
Semigroup generated by Schroedinger operator 47
Semigroup, kernel 24
Shulman property 18
Single site distribution 5 38
Single site of changing sign 40 54
Single site of long range 55
Single site potential 5 38
Singular values 47 67 69
Spectral averaging 43 59
Spectral gaps 12 14
Spectral localisation 7
Spectral measure 17
Spectral projection 8 43
Spectral shift function 46 52 67 71
SSF see "Spectral shift function"
Stationary 6
Stone's formula 60
Subadditive process 11 31
Super-trace class 47 68
Superadditive process 11 31
Symbol of Toeplitz matrix 64
Tempelman property 18
Tempered sequence 18
Toeplitz matrix 63
Trace 58
Trace, class 43 46 58 67 69
Trace, regularising 57 59 66
Ultracontractive semigroup 24
Unbounded coupling constants 6 58 66
Unique continuation property 35 37 53
van Hove property 19 28
Volume, comparison theorem 26
Volume, density 13
von Neumann algebra 16
Wegner constant 34
Wegner estimate 33 38 39
Weyl asymptotics 31 38 40 45
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