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Авторизация |
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Diaconis P. — Group Representations in Probability and Statistics |
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Предметный указатель |
18 21 47 160
15
, data on 110 145 162
, models on 168
, random walk on 18 28 58 67 72 77 86 89
, representations of 16
15
, data on 100 141
, random walk on 17 25ff 28
, representations of 15
Action of group 51
Affine group 17 30 34 90
Alternating group 45
American Psychological Association data 93
Analysis of variance 61 112 153 163
Association schemes 60
Association-measures of 102 106
Automorphisim 32
Automorphisim of designs 156
Balanced incomplete block designs 157
Bernoulli — Laplace diffusion 56 59
Bi-invariant 54
Bibliography 2 61
Bingham density 171
Borel shuffle 18 84
Branching theorem 138
Bridge 78
Burnsides lemma 135
Card shuffling 18ff 69 77ff
Cayley distance 117ff 122 123
CHARACTER 9
Character as a metric 120
Character of symmetric group 137
Character, orthogonality relations for 11
Circulant 50ff
Cities, distance data 92 142
Class functions 14 15 24 35 60
codes 46
Column stabilizer 132
Combinatorial central limit theorem 115
Condorcets rule 107
Conjugacy 14
Convolution 7
Coupling 84
Covariance 178
Covariance matrices 101
Cutoff phenomenon 18 91
Cycle notation 5
Dimension of representation 5
Direct sum decomposition 8 12
Draft lottery data 93 102ff
Ehrenfest urn 19 28 72 77 86 89
Equivalent representations 9
Exponential families and covariates 178
Exponential families from representations 167
Exponential families on sphere 170
Exponential families, theory of 175
First hit distribution 49 64ff 87ff
First time to cover all 87ff
Fisher-von Mises distribution 170ff
Fixed points 134
Fixed vector approach 121 124 126
Floyd’s game 118
Fourier inversion theorem 13
Fourier transform 7
Frobenius reciprocity 54
Gelfand pair 54ff 61ff
Grand tour 20
Group 5
Group, means and medians on 108 109 “ “Orthogonal “ “
Hamming distance 117 123
Hausdorff metric 124ff
Hollands model 172
Homogeneous space 51
Homogeneous space, data on metrics on 124
Homogeneous space, random walk on 51
Horse race data 174
Hypergroup 113
Inference for spectral analysis 115
Invariance 112 113 161
Inversions 123
Irreducible representation 5
Isotropy subgroup 51
Item analysis 145 162
k sets of an n set 56 59 97 125 126
Kazhdan — Lusztig representations 139
Kendalls tau 117ff 123 127 130
Kendalls tau as social choice function 108
Krawtchouk polynomials 58
Lengths on groups 121ff
Lottery 97ff
| Lower bounds 26 27 35 43 71 82
Luce model 174
Majorization 40 131
Mallows model 104 123
Markov chains 19 48ff 52 169
Matrix norms 119
Metrics 102ff
Metrics on homogeneous space 124
Metrics on probabilities 23 33 110
Metrics, applications of 102ff
Metrics, examples of 112ff
Metrics, invariance of 112
Multidimensional scaling 104 105
Orthogonal group 20
Orthogonal group, acting on sphere 105
Orthogonal group, data on 111
Orthogonal group, metrics on 120
Orthogonal group, random walk on 20 47
Orthogonal series estimators 168
Overhand shuffle 19 87
p-adic numbers 21
Panel study data 145 162
Partially ranked data 93 125 127 147ff
Permutation group see “Symmetric group”
Permutation representation 5 132
Product group 16
Projection pursuit 17
Projective plane 160
Q-nomial coefficients 128
Q-sort data 99
Quarternions 14 50
Radon transform 45 151
Random walk see “Affine group” “ “Orthogonal “ “
Rank tests 111
Rapidly mixing chain 88
Rayleigh test 170
Regular representation 12 120
Representations 5
Representations of 16
Representations of affine group 34
Representations of symmetric group, 3-D Chapter 7
Riffle shuffle 19 77
Robinson — Schensted — Knuth correspondence 139
Robust regression 106
Schensted correspondence 139
Schur’s lemma 7
Separation distance 75
Social choice 107
Spearmans footrule 102 114 115ff
Spearmans rho 116ff
Spectral analysis and ANOVA 153
Spectral analysis of permutations 142
Spectral analysis of time series 141
Spectral analysis on homogeneous spaces 147
Spectral analysis, inference for 143
Sphere, data on 100
Sphere, metrics on 125 126
Sphere, models on 170
Spherical functions 55 56
Strong uniform time 69 75
Subrepresentation 5
Symmetric group 5
Symmetric group, characters of 37 137
Symmetric group, data on 93
Symmetric group, metrics on 131ff
Symmetric group, random walk on 22 (see also “Card shuffling” “Transpositions”)
Symmetric group, representations of 6 36ff 131ff
Tableau 38 131
Tabloid 39 132
Tensor product 8 44
Time series analysis 141 165ff
Top in at random shuffle 69
Transitive action 51
Transpositions, random 18 36ff 73ff
Trees 21 104 105
Trivial representation 5
Two point homogeneous 59
Ulam’s distance 118ff
Unfolding hypothesis 92
Uniform distribution 10
Uniform distribution, convergence to 23 79
Uniform distribution, tests for 109 170
Upper bound lemma 24 25 53
Upper bound lemma for coupling 86
Upper bound lemma for strong uniform times 70 76
Useful fact 134
Variation distance 21 22 25 52
Weyl group 122ff
Wreath product 155 162
Young tableau see “Tableau”
Youngs rule 138 148 159
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