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SUMMARY:Limits of Polya urns with innovations - Jean Bertoin (Zurich)
DTSTART:20220907T080000Z
DTEND:20220907T090000Z
UID:TALK178484@talks.cam.ac.uk
CONTACT:Jason Miller
DESCRIPTION:We consider a version of the classical P\\'olya urn scheme whi
 ch incorporates innovations. The space $S$ of colors is an arbitrary measu
 rable set. \nAfter each sampling of a ball in the urn\, one returns $C$ ba
 lls of the same color and additional balls of different colors given by so
 me finite point process $\\xi$ on $S$. \nWhen the number of steps goes to 
 infinity\,  the empirical distribution of the colors in the urn converges 
 to the normalized intensity measure of $\\xi$\, and we analyze the fluctua
 tions. \nThe ratio $\\rho= \\E(C)/\\E(R)$ of the average number of copies 
 to the average total number of balls returned plays a key role.  
LOCATION:MR9\, Centre for Mathematical Sciences
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