Index
∗-algebra, 160
2-Schatten norm, 114
R-transform, 180
S-transform, 181
k-point correlation function, 196
absolutely continuous, 12
absolutely integrable, 13, 16
Airy function, 206, 260
Airy kernel, 206
almost sure convergence, 32, 135
almost surely, 6
amalgamated free product, 176
antichain, 215
approximation to the identity, 144
asymptotic free independence, 174
asymptotic notation, 5
asymptotically almost surely, 6
Atiyah convexity theorem, 44
augmented matrix, 133
Azuma’s inequality, 63
Bai-Yin theorem, 129, 131
Baker-Campbell-Hausdorff formula, 252
Bernoulli distribution, 11
Bernoulli ensemble, 105
Berry-Ess´ een theorem, 87, 95, 100, 101,
213
bijective proof, 122
Bochner’s theorem, 257
Borel-Cantelli lemma, 14, 34
Brown measure, 232, 233
Burgers’ equation, 153
Carleman continuity theorem, 90
Catalan number, 122
Cauchy transform, 142
Cauchy-Binet formula, 253
Cauchy-Schwarz inequality, 164
central limit theorem, 79, 86
characteristic function, 15
Chebyshev’s inequality, 17
Chernoff bound, 79
Chernoff inequality, 61
Christoffel-Darboux formula, 197
circular law, 193, 209, 224
circular unitary ensemble, 268
classical probability theory, 160
compressible, 213, 215, 218
concentration of measure, 56
condition number, 209
conditional expectation, 27
conditional probability, 27
conditional probability measure, 24
conditioning, 24, 29
convergence in distribution, 32
convergence in expectation, 135
convergence in probability, 32, 135
convergence in the sense of ∗-moments,
172
convergence in the sense of moments,
172
correlation, 58
Courant-Fischer minimax theorem, 42
covariance matrix, 86
cumulant, 180
cumulative distribution function, 12
279
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