Neuenschwander D. — Probabilities on the Heisenberg Group: Limit Theorems and Brownian Motion, Vol. 163 :: Электронная библиотека попечительского совета мехмата МГУ

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Neuenschwander D. — Probabilities on the Heisenberg Group: Limit Theorems and Brownian Motion, Vol. 163

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Название: Probabilities on the Heisenberg Group: Limit Theorems and Brownian Motion, Vol. 163

Автор: Neuenschwander D.

Аннотация:

The Heisenberg group comes from quantum mechanics and is the simplest non-commutative Lie group. While it belongs to the class of simply connected nilpotent Lie groups, it turns out that its special structure yields many results which (up to now) have not carried over to this larger class. This book is a survey of probabilistic results on the Heisenberg group. The emphasis lies on limit theorems and their relation to Brownian motion. Besides classical probability tools, non-commutative Fourier analysis and functional analysis (operator semigroups) comes in. The book is intended for probabilists and analysts interested in Lie groups, but given the many applications of the Heisenberg group, it will also be useful for theoretical phycisists specialized in quantum mechanics and for engineers.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1996

Количество страниц: 139

Добавлена в каталог: 04.07.2008

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Предметный указатель

Accompanying laws theorem      15 99
Accompanying system      99
Admissible mapping      15
Approximate martingale      6
Associated random measure      82
Atiyah — Singer theorems      2
Bernstein theorem      32
Braided group      6
Campbell — Hausdorff formula      9
Canonical coordinates      99
Capacity      22
Cartan subalgebra      29
Cauchy distribution      2
Central limit theorem      19 38 73 79
Compact group      98
Complete convergence      106
Composition of quadratic forms      9
Cone      26 27 56
Continuous convolution hemigroup      14 100 101
Continuous convolution semigroup      7 13 99 101
Contracting automorphism      17
Contracting automorphism group      40 41
Convergence of types theorem      19 20 39 90
Convolution operator      8
Cramer — Levy theorem      30
Descending central series      8
Diamond group      102
Dilatation      10 39 121
Discrete subgroup      98
Domain of attraction      16 40 41 86 87 89
Domain of normal attraction      16 37 86
Domain of partial attraction      16
Donsker invariance principle      6
Doob convergence theorem      122
Double point      73
Ergodic sequence      111
Euclidean motion group      98 102
Evolution equation      15
Exchangeable sequence      112
Exponential Lie group      11 13
Finite group      29
Free simply connected step 2-nilpotent Lie group      9
Freidlin — Ventsel theory      58 65
Full probability measure      38 88 89
Gateaux differential      66
Gaussian generating distribution      11
Gaussian measure      11 30 32 37 39 40 44 75 96 100
Gaussian random variable      11
Gaussian semigroup      11 29 30 38
Generating distribution      8
Generating distribution without Gaussian component      11
Generating family      15 101
Green function      50 72
Group of type H      9
Hausdorff measure      71
Heavy trimming      39
Heisenberg commutation relation      3
Heisenberg uncertainty principle      3
Hermitean hypergroup      98
Hilbert — Lie group      6
Holder inequality      36 106
Homogeneous dimension      10 57
Homogeneous norm      10
Hunt function      99
Hunt theory      22
Hypergroup      98
Infinitely divisible measure      12 13 97 99 101
Infinitesimal generator      8
Integration by parts for semimartingales      31
Intermediate trimming      39
Invariance group      39 88
Invariant set      111
Iwasawa decomposition      9
Jacobi identity      8
Killed Brownian motion      53
Killing rate      54
Killing set      53 54
Kochen — Stone Borel — Cantelli lemma      65
Kohn Laplacian      11 38
Kronecker lemma      102
L — S-full probability measure      20 38 86 112 115 118 120
Lagrangian multiplier      66
Laplacc operator      11
Law of large numbers for exchangeable sequences      112
Law of large numbers, Baum — Katz      106 109
Law of large numbers, Bose — Chandra      112
Law of large numbers, Erdos — Renyi      67
Law of large numbers, Hsu — Robbins — Erdos      106
Law of large numbers, Kolmogorov      74 84 95 101 106
Law of large numbers, Komlos      82
Law of large numbers, Marcinkiewicz — Zygmund      102 103 104 105 106 108 109

Law of the iterated logarithm, Chover      112
Law of the iterated logarithm, Chung maximal      61
Law of the iterated logarithm, Hartman — Wintner      73
Law of the iterated logarithm, Levy asymptotic      58
Law of the iterated logarithm, Levy local      58
Lebesgue needle      56
Levy construction of first kind      89
Levy construction of second kind      89
Levy inequality      108
Levy measure      11
Levy stochastic area process      31 37
Levy — Hincin formula      11
Lie — Trotter product formula      13
Light trimming      39 89
Limit statute      82 105
Lindeberg theorem      17 33
Lipschitz continuous hemigroup      14 101
Ljapunov Theorem      35
Local centering      98 99
Location operator      3
Martingale      3 24 37 122
Maximal lemma      58 78
Maximum principle      22
Minkowski multiplication      6
Mixing sequence      6 112
Modulus trimming      39
moment      37 73 101 102 105 106 109
Momentum operator      3
Normal measure      31
Norming sequence      16 41 90
Occupation measure      72
Operator stable probability measure      13
Order statistics      88 89
Ottaviani inequality for homogeneous groups      113
Outlier resistance      39
p-adic group      6
Poincare criterion      27
Poisson approximation theorem      15
Poisson measure      7
Poisson semigroup      7 11 29
Polar coordinate decomposition      40 90
Positive graduation      10
Potential kernel      22
Primitive distribution      11 13
Prohorov distance      88
Prohorov theorem      42 99
Pseudo inner product      38
Pseudo-distance      45
Quantum group      6
Rate of convergence      73 106
Regular boundary      21
Right gradient      12
Robust statistics      39
Root set      12
Semigroup without Gaussian component      11 86 87 88 112 118 120
Semisimple Lie group      10 29
Semistable semigroup      13 29 31 121
Skew-symplectic mapping      38 86 87 120
Skorohod topology      37
Slowly varying function      87
Spectral decomposition      31
Stable semigroup      13 16 29 31 38 39 40 86 88 89 112 121
Standard Brownian motion      11 32 35
Statistics of directional data      1
Stirling formula      41
Stratified group      10
Strict domain of attraction      16 86
Strict domain of normal attraction      38 87 116
Strict domain of partial attraction      16
Strictly semistable semigroup      13 115 120 121
Strictly stable semigroup      13 38 86 112 116 118 121
Strictly universal law      16
Strongly root compact group      12
Sturm — Liouville equation      62
Subadditive process      24
Subsequence principle      82 105
Support function      6
Symmetric space      29 98
Symplectic form      38
Symplectic group      38
Symplectic mapping      38 86 87 120
Tauberian theorem      24
Three-series theorem      121 122
Trimmed product      40 89
Trimmed sum      39
Truncated random variable      44 91
Universal law      16 85 86
Wiener sausage      24 44
Wiener test      24
Zero-one law, Blumenthal      24 26
Zero-one law, Gallardo      24
Zero-one law, Kolmogorov      118 119 120

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