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Diaconis P. — Group Representations in Probability and Statistics
Diaconis P. — Group Representations in Probability and Statistics

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Название: Group Representations in Probability and Statistics

Автор: Diaconis P.

Аннотация:

This monograph is an expanded version of lecture notes I have used over the past eight years.. I first taught this subject at Harvard's Department of Statistics 1981-82 when a version of these notes were issued. I've subsequently taught the subject at Stanford in 1983 and 1986. I've also delivered lecture series on this material at Ohio State and at St.. Flour..
This means that I've had the benefit of dozens of critics and proofreaders the graduate students and faculty who sat in. Jim Fill, Arunas Rudvalis and Hansmartin Zeuner were particularly helpful.
Four students went on to write theses in the subject - Douglas Critchlow, Peter Matthews, Andy Greenhalgh and Dan Rockmore. Their ideas have certainly enriched the present version.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 198

Добавлена в каталог: 01.07.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$GL_n$      18 21 47 160
$\mathbb{Z}_2^n$      15
$\mathbb{Z}_2^n$, data on      110 145 162
$\mathbb{Z}_2^n$, models on      168
$\mathbb{Z}_2^n$, random walk on      18 28 58 67 72 77 86 89
$\mathbb{Z}_2^n$, representations of      16
$\mathbb{Z}_n$      15
$\mathbb{Z}_n$, data on      100 141
$\mathbb{Z}_n$, random walk on      17 25ff 28
$\mathbb{Z}_n$, 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 $\mathbb{Z}_n$      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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