332 INDEX
irreducible —, 84
symmetric —, 85
transition probability of —, 56
Minkowski functional, 8
moderate deviation, 222, 248
modification of stochastic processes, 35
continuous modification, 35, 52
modified Bessel equation, 297
multinomial inequality, 181
non-negative operator, 93, 98
occupation measure, 36
Orlicz norm, 309
Orlicz space, 309
Parseval identity, 299, 301, 302
period of random walk, 134
periodic function, 134, 301, 302
Plancherel-Parseval theorem, 54, 302
Poisson process, 22
polymer models, 111
positively balanced set, 8
probability of no return, 138
projection operator, 315
Prokhorov criterion, 310
Radon measure, 44
random walk, 133
random walk in random scenery, 174, 292
range of random walk, 133, 160, 177
rapidly decreasing function, 93, 300, 301
rate function, 2
recurrence, 138
renormalization, 48
resolution of identity, 97, 315, 317
resolvent approximation, 136
resolvent equation, 306
resolvent random walk, 136
reverse Markov inequality, 57
Schwartz space, 94, 300
self-adjoint operator, 61, 209, 314
function of self-adjoint operator, 318
self-attracting polymer, 26
self-repelling polymer, 26
semi-bounded operator
lower —, 315
upper —, 94, 315
semi-group, 92
simple random walk, 134, 145
small ball probability, 23
Sobolev inequality, 303
Sobolev space, 303
spectral decomposition, 314
spectral integral, 96, 316
spectral integral representation, 61, 210,
314, 317
spectral measure, 97, 315
spherically symmetric function, 131
steep function, 3
sub-additive functional of random walk, 178
sub-additive sequence, 19
deterministic —, 19
sub-additive stochastic process, 21
sub-additivity, 1, 91, 117
sub-critical dimensions, 145
super-critical dimensions, 145, 173
symmetric operator, 92, 94, 208, 314
thick point, 173
topological dual space, 107
transience, 138
triangular approximation, 49, 50, 161, 192,
258
uniform exponential integrability, 18
uniform tightness, 8, 139, 310
Varadhan’s integral lemma, 6
Wiener sausage, 249, 291, 293, 294
Young function, 309
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