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SUMMARY:The simple harmonic urn - Stas Voklov (Univ.  Bristol)
DTSTART:20091013T150000Z
DTEND:20091013T163000Z
UID:TALK19780@talks.cam.ac.uk
CONTACT:Berestycki
DESCRIPTION:The simple harmonic urn is a discrete-time stochastic process 
 approximating the phase portrait of the simple harmonic oscillator. This u
 rn is a version of a two-colour generalized Polya urn with negative-positi
 ve reinforcements\, and in a sense it can be viewed as a "marriage" betwee
 n the Friedman urn and the OK Corral model\, where we restart the process 
 each time it hits a border by switching the colours of the balls. We show 
 the transience of the process using various couplings with birth and death
  processes and renewal processes. It turns out that the simple harmonic ur
 n is just barely transient\, as a minor modification of the model makes it
  recurrent\, and for a good reason\, as the embedded urn process is\, in f
 act\, a Lamperti-type random walk. We also show links between this model a
 nd oriented percolation\, as well as a few other interesting processes. Th
 is is joint work with E. Crane\, N. Georgiou\, R. Waters and A. Wade. 
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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