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Slade G. — The Lace Expansion and Its Applications
Slade G. — The Lace Expansion and Its Applications

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Название: The Lace Expansion and Its Applications

Автор: Slade G.

Аннотация:

The lace expansion is a powerful and flexible method for understanding the critical scaling of several models of interest in probability, statistical mechanics, and combinatorics, above their upper critical dimensions. These models include the self-avoiding walk, lattice trees and lattice animals, percolation, oriented percolation, and the contact process. This volume provides a unified and extensive overview of the lace expansion and its applications to these models. Results include proofs of existence of critical exponents and construction of scaling limits. Often, the scaling limit is described in terms of super-Brownian motion.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 232

Добавлена в каталог: 23.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Backbone      77 82 132 153 186
Ballistic      11 61
BK inequality      99
BOND      5
Branching random walk      171
Brownian motion      5 58
Bubble condition      14 41 54
Bubble diagram      14
Bulk boundary condition      138
Canonical measure      201
Cauchy distribution      58
Central limit theorem      3
Central limit theorem, local central limit theorem      59 65 146
Cluster expansion      57
Compatible      24 177 192
Complete graph      133
Conformal invariance      70
Connected graph      22 78
Connected in      100
Connected through      100
Connective constant      8 53 64
Contact process      161
Contact process, approximation by oriented percolation      163
Continuum percolation      129
Convolution      2
correlation length      13 88 126
Correlation length of order      2 52
Critical exponent, branching random walk      174 186
Critical exponent, contact process      142 144 165
Critical exponent, lattice animal      69 81
Critical exponent, lattice tree      68 69 195
Critical exponent, percolation      89 96 125 198
Critical exponent, self-avoiding walk      9 11 42 46
Critical point, collapse transition      63
Critical point, contact process      162 166
Critical point, finite graph      134 135
Critical point, lattice tree      68
Critical point, oriented percolation      142 146
Critical point, percolation      88 129
Critical point, self-avoiding walk      12
Critical point, simple random walk      4
cube      136
Differential equality      54 75
Differential inequality, lattice tree      71
Differential inequality, oriented percolation      144
Differential inequality, percolation      91
Differential inequality, self-avoiding walk      14
Diffusion constant      59 64
Domb — Joyce model      8
Double connection      81 111 152
Double expansion      75 210
EDGE      5 22
Edge, compatible      24 79
Extrapolation principle      97
Finite box      138
Finite-dimensional distributions      203 208 210
Fisher relation      13 69
Fixed-point method      59
Fourier transform      2
Free energy      126
Galton — Watson branching process      91 172
Gap exponent      126
Generating function      2
Graph      22
Graph, connected      22 78
Green function      3
Green vertex      89
Hyperscaling      91 138 143
Incipient infinite cluster, oriented percolation      147
Incipient infinite cluster, percolation      130
Incipient infinite cluster, scaling limit      199 209
Inclusion-exclusion, lattice tree      72 81
Inclusion-exclusion, oriented percolation      152
Inclusion-exclusion, percolation      110
Inclusion-exclusion, self-avoiding walk      16 19 54
Infinite self-avoiding walk      61
Infrared bound      14 47 126 144 164
Integrated super-Brownian excursion      189
Ising model      IX
Lace      24 78
Lace expansion on a tree      65 75 210
Lace expansion, contact process      167
Lace expansion, contact process, diagrammatic bounds      169
Lace expansion, inductive approach      57 60 63 145
Lace expansion, lattice animal      81
Lace expansion, lattice tree      77
Lace expansion, lattice tree, diagrammatic estimates      83
Lace expansion, lattice tree, expansion via laces      78
Lace expansion, lattice tree, inclusion-exclusion      81
Lace expansion, oriented percolation      151
Lace expansion, oriented percolation, diagrammatic estimates      158
Lace expansion, oriented percolation, expansion via laces      154
Lace expansion, oriented percolation, inclusion-exclusion with multiple expectations      156
Lace expansion, oriented percolation, inclusion-exclusion with single expectation      152
Lace expansion, percolation      109
Lace expansion, percolation, diagrammatic estimates      121
Lace expansion, self-avoiding walk      19
Lace expansion, self-avoiding walk, convergence      41
Lace expansion, self-avoiding walk, diagrammatic estimates      31
Lace expansion, self-avoiding walk, expansion via laces      21
Lace expansion, self-avoiding walk, inclusion—exclusion      19
Lambert W function      172
Lattice animal      69
Lattice tree      67
Lattice tree, mean-field      171
Lattice tree, weakly self-avoiding      180
Logarithmic correction      10 11 13
magnetization      89 142
Mean-field      14 54 70 90 95 127 135 144 163 165 171 195 198
Mean-square displacement      3 11 28 58 62
Memory      29
Memory, memory-two      28
Moment measure      184 189 200 203 206 208
Nearest-neighbour model      1
Nested expectation      101 115
Network      63
Nineteen      125
Number of clusters per vertex      89
Oriented percolation      141
Ornstein — Zernike decay      13
Percolation      87
Percolation on finite graph      133
Percolation probability      90 142
Periodic boundary condition      136 139
Phase transition, branching process      91
Phase transition, contact process      161
Phase transition, oriented percolation      141
Phase transition, percolation      87
Phase transition, polymer collapse      62
Pivot algorithm      11 68
Pivotal bond      82 99
Poisson branching      172
Polymer, branched      67
Polymer, collapse transition      62
Polymer, linear      7
Polymer, network      63
R-point function, branching random walk      177
R-point function, contact process      210
R-point function, incipient infinite cluster      209
R-point function, lattice tree      71 196 210
R-point function, oriented percolation      207
R-point function, percolation      199
Radius of gyration      69
Random graph      133
Sausage      110
Scaling limit      5 13 58 69 81 132 183 194 198 200 202 208
Scaling window      134 136 139
Self-attracting walk      62
Self-avoiding walk      7
Self-avoiding walk, 1—dimensional      61
SHAPE      175
Simple random walk      1
Simple random walk, intersections      5
Simple random walk, recurrent      4
Simple random walk, transient      4
Single end      132
Skeleton      72 176
SLE (Schramm — Loewner evolution)      10 13 70
Spread-out model      1
Square condition      72 75
Square diagram      72
Star polymer      63
Subadditivity      8 68 99
Subshape      176
Super-Brownian motion      183 201
Survival probability      148 209
susceptibility      4 12 41 68 71 75 90 99 130 133 141 162 186
Tauberian theorem      75
Tightness      209 210
Triangle condition      95 125 129 135 145 165
Triangle diagram      84 95 121 135 145 165
Two-point function, branching random walk      174 186
Two-point function, contact process      162 169
Two-point function, incipient infinite cluster      132
Two-point function, lattice animal      82
Two-point function, lattice tree      68 70 77
Two-point function, mean-field lattice tree      171
Two-point function, oriented percolation      143
Two-point function, percolation      88 103 127
Two-point function, self-avoiding walk      2 60
Two-point function, simple random walk      3
Universality      6 10 69 128 180
Upper critical dimension      6
Upper critical dimension, contact process      163 166
Upper critical dimension, lattice tree      70
Upper critical dimension, oriented percolation      143 157
Upper critical dimension, percolation      91 116
Upper critical dimension, self-avoiding walk      14 58
Vertex factor      55 64 149 196 199 208
Watermelon network      65
Weakly self-avoiding lattice trees      180
Weakly self-avoiding walk      8 10 57 61
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