Theoretical Statistics and Mathematics Unit, ISI Delhi

September 21, 2011 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Debleena Thacker,
Indian Statistical Institute, Delhi

Title:
Urn Models on One-dimensional Integer Lattice.

Abstract of Talk

In this talk we will present a new urn model consisting of
balls of infinite but countably many colors which we index by the
integers. We will consider two special replacement matrices, one
arriving from the right shift operator, and the other arriving from
the simple symmetric random walk on the one dimensional integer
lattice. We show using martingale techniques that in both the cases
the expected proportion of colors converges to a standard normal
distribution after an appropriate centering and scaling by $\sqrt{\log
n}$. This shows that even though the associated Markov chain has
different qualitative properties, namely one is transient and the
other is null recurrent, the infinite color urn models have same
asymptotic behavior. This is in sharp contrast to what is generally
observed for finite color urn models.