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CATEGORIES:Probability
SUMMARY:Lifetime of relativistic diffusions - Ismael Baill
eul (Cambridge)
DTSTART;TZID=Europe/London:20101123T163000
DTEND;TZID=Europe/London:20101123T173000
UID:TALK26756AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/26756
DESCRIPTION:Relativistic diffusions are models of random motio
n in spacetime of an object moving with a speed le
ss than the speed of light. These processes are th
e Lorentzian analogues of Brownian motion in a Rie
mannian context. In so far as they are defined in
purely geometric terms\, it is very likely that pa
rt (or all?) of the geometry of the ambient spacet
ime may be recovered from the probablistic behavio
ur of these processes. In a Riemannian setting\, t
his probabilistic view on geometry is well-illustr
ated by Weyl and Pleyel formulas for the heat kern
el of Brownian motion where local and global infor
mations about the geometry appear.\n\nWe shall inv
estigate in this talk one aspect of this geometry/
probability correspondence. Dating back to Penrose
and Hawking's results\, it is now well-establishe
d that the appearance of singularities in Einstein
's theory of gravitation is unavoidable under quit
e natural assumptions. Although there is no defini
tive agreement on what should be called a singular
ity of spacetime\, a largely used notion of singul
arity is the existence in spacetime of incomplete
geodesics. Is there a link between geodesic and pr
obabilistic incompleteness? This will be the main
question will shall adress. \n\n\nhttp://www.stats
lab.cam.ac.uk/~ismael/
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Berestycki
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