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From:  Date: Fri, 12 Feb 1999 12:26:39 +0000

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 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               ******************************************               *2.05pm, Room S27, Statistical Laboratory*               ****************************************** Friday, 19th February --------------------- 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. ------------------------------------------------------------------------ Friday, 5th March ----------------- Ravi Mazumdar (University of Essex) TO BE ANNOUNCED                        ***************************                        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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%