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CATEGORIES:Probability
SUMMARY:The Laplacian on some finitely ramified self-confo
rmal circle packing fractals and Weyl's asymptotic
s for its eigenvalues - Naotaka Kajino (Kobe Unive
rsity\, Japan)
DTSTART;TZID=Europe/London:20170704T161500
DTEND;TZID=Europe/London:20170704T171500
UID:TALK73170AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/73170
DESCRIPTION:The purpose of this talk is to present the speaker
's recent research\nin progress on the constructio
n of a ``canonical'' Laplacian on finitely\nramifi
ed circle packing fractals invariant with respect
to a family of\nMoebius transformations and on Wey
l's asymptotics for its eigenvalues.\n\nIn the sim
plest case of the Apollonian gasket\, the speaker
has obtained\nan explicit expression of a certain
canonical Dirichlet form in terms of the\ncircle p
acking structure of the fractal. Our Laplacian on
a general circle\npacking fractal is constructed b
y adopting the same kind of expression\nas the def
inition of a (seemingly canonical) strongly local
Dirichlet form.\nWeyl's eigenvalue asymptotics for
this Laplacian has been also established\nin some
important examples including the Apollonian gaske
t\, and the proof\nof this result heavily relies o
n ergodic-theoretic analysis of a Markov\nchain on
\nthe space of ``shapes of cells'' resulting from
a suitable cellular\ndecomposition\nof the fractal
.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Perla Sousi
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