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SUMMARY:The Many Body Cercignani's Conjecture. - Dr Amit Einav (DPMMS)
DTSTART:20141105T160000Z
DTEND:20141105T170000Z
UID:TALK55629@talks.cam.ac.uk
CONTACT:Eavan Gleeson
DESCRIPTION:One of the most influential equations in the kinetic theory of
  gases is the so-called Boltzmann equation\, describing the time evolution
  of the probability density of a particle in dilute gas. While widely used
 \, and intuitive\, the Boltzmann equation has no formal validation from Ne
 wtonian laws\, in macroscopic time scales.\nIn 1956 Marc Kac presented an 
 attempt to solve this problem in a particular settings of the spatially ho
 mogeneous Boltzmann equation. Kac considered a stochastic linear model of 
 N indistinguishable particles\, with one-dimensional velocities\, that und
 ergo a random binary collision process. Under the property of 'chaoticity'
  Kac managed to show that when one takes the number of particles to infini
 ty\, the limit of the first marginal of the N-particle distribution functi
 on satisfies a caricature of the Boltzmann equation\, the so-called Boltzm
 ann-Kac equation. Kac hoped that using this mean field approach will lead 
 to new results in the convergence to equilibrium of the limit equation usi
 ng the simpler\, yet dimension dependent\, linear ODE.\nIn our talk we wil
 l introduce Kac's model and the concept of Chaoticity. We will then discus
 s possible trends to equilibrium and review recent results in the matter. 
 Time permitting\, we will describe related research that has been done rec
 ently in connection to the above.\n\n
LOCATION:MR14\, Centre for Mathematical Sciences
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