Kac walk
E92907
The Kac walk is a probabilistic model introduced by mathematician Mark Kac to study the approach to equilibrium in kinetic theory via a simplified random process.
Statements (30)
| Predicate | Object |
|---|---|
| instanceOf |
model in kinetic theory
ⓘ
probabilistic model ⓘ stochastic process ⓘ |
| assumes |
binary collisions
ⓘ
energy conservation in collisions ⓘ |
| basedOn | random collisions between particles ⓘ |
| describes | evolution of velocity distribution of particles ⓘ |
| field |
kinetic theory
ⓘ
probability theory ⓘ statistical mechanics ⓘ |
| hasDimension | velocity space of many particles ⓘ |
| hasProperty |
Markovian
ⓘ
conservative dynamics ⓘ time-homogeneous ⓘ |
| introducedBy | Mark Kac ⓘ |
| modelType | simplified random process ⓘ |
| namedAfter | Mark Kac ⓘ |
| purpose |
to model relaxation to equilibrium in gases
ⓘ
to study approach to equilibrium ⓘ |
| relatedTo |
Boltzmann equation
ⓘ
Boltzmann–Kac equation ⓘ entropy production ⓘ kinetic theory of gases ⓘ propagation of chaos ⓘ spectral gap estimates ⓘ |
| studiedIn |
mathematical physics
ⓘ
probability on high-dimensional spaces ⓘ |
| typicalStateSpace | sphere in high-dimensional Euclidean space ⓘ |
| usedFor |
rigorous study of convergence to equilibrium
ⓘ
testing ideas in kinetic theory on simplified models ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.