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| Smythe R.T. — First-Passage Percolation on the Square Lattice |
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| Предметный указатель |
"Stiff" percolation 167
Asymmetric oriented percolation 167
Average cluster size 59
Barrier 72ff 83 99 151
Bernoulli percolation 3 28ff 138 156
Birkhoff ergodic theorem 143 183 185
BOND 1
Bond percolation 2 14
Bond, closed 2 28 112 138
Bond, cluster 5 30 46 50 109 139
Bond, open 2 28 109 112 139
Bond, oriented 2 158 167
Bond, unoriented 2
Circuit (graph) 5 9 35 41 42 139
Cluster see "Bond" "Graph"
Connectivity constant 24 31 49 161 168
Covariant event 13 36
Critical probability 29ff 43 62 109 112 138 167 170
Dual see "Graph" "Sponge"
First-passage time 3 6 63ff 78ff 159
First-passage time, cylinder 64 86 113 118
FKG inequality 12 37ff 177
Graph 5
Graph, cluster 5
Graph, component 5
Graph, connected 5
Graph, cut set 5 9 139
Graph, dual 8
Hammersley's upper bound 49
Harris' cluster theorem 50
Harris' lower bound 42
Height process 128 146ff 168 173
Infinite zero cluster 50
Kesten — Hammersley theorem 20 85 99
Kingman's ergodic theorem 17 79 87 91 183
Komlos' theorem 186
Lattice (algebraic) 13 177
Lattice (graph) 1
Lattice (graph), covering 2
Lattice (graph), dual 34 47 74 139 152
| Lattice (graph), square 3 24 158
Mauldon's model 167
Mean cluster size 51
Monte Carlo results 62 117 163
Morgan — Welsh model 158 162 172
Oriented percolation 2 158ff
Path 5
Path, connected 7
Path, cylinder 64
Path, self-avoiding 5 26 49 63 94 96 104 136 165 168
Path, three-way cylinder 65 85
Percolation probability 29
Percolation process 1 7
Reach process 101ff 110 159 172
Renewal function 101
Renewal theory 101ff 168 172
Richardson's model 175
route 6 76ff 125
Route, existence 72ff
Route, height 128
Route, length 128ff 168 173
Seymour — Welsh theorem 28 44
Site 1
Site percolation 2
Sponge 9 30ff 35 44ff 61 112 150
Sponge, dual 10 34
Strong renewal theorem 172
Subadditive function 17 81 107 116
Subadditive process 16 25 54 78 98 171 183
Subadditive process, two-dimensional 18 54 188
time constant 17 79ff 111ff 160 170 183
Time constant, continuity of 154ff 172
Time coordinate 6 67
Time coordinate, negative 75ff 94ff
Time state 6 118 126 156
Time state, shifted 121 135
Travel time 6
Truncation 107 122ff 154 161
Unrestricted process 63
Weak renewal theorem 101 105 172
Whitney dual graph 8 139
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