UNIVERSITY OF CAMBRIDGE
DEPARTMENT OF PURE MATHEMATICS AND MATHEMATICAL STATISTICS
STATISTICAL LABORATORY
16 MILL LANE, CAMBRIDGE CB2 1SB
Tel: (01223) 337958
Fax: (01223) 337956
SEMINARS
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*2.05pm, Room S27, Statistical Laboratory*
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Friday, 19th February
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James Taylor (University of Sussex)
THE MULTIFRACTAL STRUCTURE OF GALTON-WATSON BRANCHING MEASURE
Branching measure ($\mu$) can be thought of as the result of a flow
down the tree in which a unit mass at the root divides among the branches
each time it comes to a fork. This produces a random measure on the space
of infinite paths from the root of the tree. A natural metric on the space
of paths is given by $d(x.y) = exp (-n)$, where $n$ is the largest level
such that $x$ and $y$ have common paths from the root to level $n$. If
$m > 1$ is the expected number of branches from each node and
$\alpha = \log m$, it is known that, on a typical path $x$ of the ball
$B(x,r)$ of radius $r$ centred on $x$ is of order $r^\alpha$ as $r$
decreases to $0$. The multifractal problem seeks to investigate the
exceptional sets where $(\mu)B(x,r)$ behaves like $r^\beta$
as $r \rightarrow 0$. For $\beta$ different to $\alpha$ such sets will
have zero measure, but we should decide when they are not empty - and then
how big they are in some appropriate sense.
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Friday, 5th March
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Ravi Mazumdar (University of Essex)
TO BE ANNOUNCED
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ALL INTERESTED ARE WELCOME
Updated lists of Statistical Laboratory seminars can be found at
http://www.statslab.cam.ac.uk/Dept/seminars.html
Susan Pitts
Organizer, Stats Lab Seminars
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