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We consider a number of independent Brownian motions in a bounded domain
in Rd running until time t and look at their intersection set, i.,e.
points which are hit by all the motions before time t. There is a measure
lt supported on this intersection set which counts the intensity of the
intersections and this is called the Brownian intersection measure. We
derive large t asymptotics of this measure in terms of a large deviation
principle in the set of finite measures on B. The rate function is
explicit and gives some direct meaning of the intersection measure as
pointwise product of the occupation measures of individual Brownian
motions. Our result is in fact an extension of Donsker-Varadhan large
deviations to a non-linear setting.
This is joint work with Wolfgang Koenig (Berlin).
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