Stanislav Volkov (Centre for Mathematical Sciences, Lund University, Sweden)
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Consider a graph G with a subset of "sick" vertices called "the border". A particle released from the origin performs a random walk on G until it comes in the direct contact with a sick particle, at which point it becomes sick itself, and stops walking, thus increasing "the sick border" by one point. A new particle is then released from the origin, and the process repeats, until the origin itself becomes a part of the border. We are interested in the total number xi of particles to be released by this final moment. Incidentally, this model, inspired by personal communications with Yuval Peres (Microsoft), can be viewed as a generalization of the OK Corral model considered previously by Sir John Kingman and myself. (Based on the joint work with Debleena Thacker, Uppsala).