topics in propagation of chaos
alain-sol sznitman
table des matières
a. s. sznitman: "topics in propagation of chaos"
chapter o. introduction 167
chapter i. generalities and first examples
1) a laboratory example 172
2) some generalities 177
3) examples:
a) our laboratory example 181
b) uniform measure on the sphere of radius √n in r^n 181
c) variation on a theme 182
d) symmetric self exclusion process 183
e) reordering of brownian motions 187
f) colored particles and nonlinear process 190
g) loss of markov property and local fluctuations 191
h) tagged particle: a counterexample 193
chapter ii. a local interaction leading to burgers equation
1) a warm up calculation 195
2) the n-particle system and the nonlinear process 198
3) the propagation of chaos result 203
4) tightness estimates 209
5) reordering of the interacting particle system 215
chapter iii. the constant mean free travel time regime
1) annihilating brownian spheres 218
2) limit picture for chain reactions in the constant mean free travel time regime 230
3) some comments 236
chapter iv: uniqueness for the boltzmann process
1) wild's formula 238
2) uniqueness for the boltzmann process 243
referencestopics in propagation of chaos
alain-sol sznitman
table des matières
a. s. sznitman: "topics in propagation of chaos"
chapter o. introduction 167
chapter i. generalities and first examples
1) a laboratory example 172
2) some generalities 177
3) examples:
a) our laboratory example 181
b) uniform measure on the sphere of radius √n in r^n 181
c) variation on a theme 182
d) symmetric self exclusion process 183
e) reordering of brownian motions 187
f) colored particles and nonlinear process 190
g) loss of markov property and local fluctuations 191
h) tagged particle: a counterexample 193
chapter ii. a local interaction leading to burgers equation
1) a warm up calculation 195
2) the n-particle system and the nonlinear process 198
3) the propagation of chaos result 203
4) tightness estimates 209
5) reordering of the interacting particle system 215
chapter iii. the constant mean free travel time regime
1) annihilating brownian spheres 218
2) limit picture for chain reactions in the constant mean free travel time regime 230
3) some comments 236
chapter iv: uniqueness for the boltzmann process
1) wild's formula 238
2) uniqueness for the boltzmann process 243
references