Cucker-Smale flocking particles with multiplicative noises: stochastic mean-field limit and phase transition
In this paper, we consider the Cucker-Smale flocking particles which are subject to the same velocity-dependent noise, which exhibits a phase change phenomenon occurs bringing the system from a "non flocking" to a "flocking" state as the strength of noises decreases. We rigorousl...
Saved in:
| Main Authors | , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
28.11.2017
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Summary: | In this paper, we consider the Cucker-Smale flocking particles which are
subject to the same velocity-dependent noise, which exhibits a phase change
phenomenon occurs bringing the system from a "non flocking" to a "flocking"
state as the strength of noises decreases. We rigorously show the stochastic
mean-field limit from the many-particle Cucker-Smale system with multiplicative
noises to the Vlasov-type stochastic partial differential equation as the
number of particles goes to infinity. More precisely, we provide a quantitative
error estimate between solutions to the stochastic particle system and
measure-valued solutions to the expected limiting stochastic partial
differential equation by using the Wasserstein distance. For the limiting
equation, we construct global-in-time measure-valued solutions and study the
stability and large-time behavior showing the convergence of velocities to
their mean exponentially fast almost surely. |
|---|---|
| DOI: | 10.48550/arxiv.1711.10371 |