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Department of Statistics and Department of Mathematics Monday, December 2, 2002 3:30 PM in REC 113 Professor Anastasia A. Ruzmaikina Purdue University will speak on The Characterization of Invariant Measures at the Leading Edge for Particle Systems in One Dimension Abstract We consider the space of locally finite configurations of infinitely many particles on a negative half-line with the first particle at zero. At discrete moments of time, each particle in a configuration performs an independent, identically distributed random jump. We are interested in classifying the probability measures in the space of all configurations such that the probability distribution of gaps behind the leader and the probability distribution of the number of particles within given distances behind the leader do not change in time. The main result is that any such probability measure is supported on the Poisson processes with densities of the form s exp(-sx), where s > 0.
Joint work with M. Aizenman and P. Contucci.
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