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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, February 10, 2004}
\centerline{Sequoia Hall Room 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Martin Zerner}
\centerline{\sl Stanford University}
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\centerline{\bf How tall must trees be to fill the sky?}

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Abstract:

Is there a forest with the following two properties?
1. The average height of the trees in that forest is 30 feet.
2. After raising the level of soil in the forest 
   uniformly by one foot the forest still looks
   the same as before. In particular, the average height
   of the trees is still 30 feet.

The answer is "yes" iff the dimension of the space is at least 3,
as we show in recent joint work with M. Bramson and O. Zeitouni.
We shall use such a forest to construct an example of
a random environment in which a random walk disobeys a
certain 0-1 law. This is closely related to several open problems
in the area of random walks in random media.

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