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CATEGORIES:Analysis seminar
SUMMARY:The mathematical study of interacting systems. - E
inav\, Amit\; Durham University
DTSTART:20220926T140000Z
DTEND:20220926T150000Z
UID:TALK4972AT
URL:/talk/index/4972
DESCRIPTION:We are surrounded by systems that revolve around m
any elements and the interactions between them: th
e air we breathe\, the galaxies we watch\, herds o
f animal roaming the African planes and even us an
d – trying to decide on whom to vote for.\nAs comm
on as such systems are\, their mathematical invest
igation is far from simple. Motivated by the reali
sation that in most cases we are not truly interes
ted in the individual behaviour of each and every
element of the system but in the average behaviour
of the ensemble and its elements\, a new approach
emerged in the late 1950s - the so-called mean fi
eld limits approach. The idea behind this approach
is fairly intuitive: most systems we encounter in
real life have some underlying pattern – a correl
ation relation between its elements. Modelling a g
iven phenomenon with an appropriate Liouville equa
tion together with such correlation relation yield
s a limit equation that describes the behaviour of
an average limit element of the system which will
help us\, one could hope\, understand better the
original ensemble.\nIn our talk we will give the b
ackground to the formation of the ideas governing
the mean field limit approach and focus on one of
the original models that motivated the birth of th
e field – Kac’s particle system. We intend to intr
oduce Kac’s model and its associated (asymptotic)
correlation relation\, chaos\, and explore attempt
s to infer information from it to its mean field l
imit – The Boltzmann-Kac equation.\n
LOCATION:WATN-LT C (G24)
CONTACT:Yuzhao Wang
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