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Rate of Convergence and Large Deviation for the Infinite Color Pólya Urn Schemes
**

**Abstract :**
In this work we consider the *infinite color urn model* associated with a bounded increment random walk
on ℤ^{d}. This model was first introduced by Bandyopadhyay and Thacker (2013).
We prove that the rate of convergence of the
expected configuration of the urn at time n with appropriate centering and scaling is of the order
O((log n)^{-1/2}).
Moreover we derive bounds similar to the classical Berry-Essen
bound. Further we show that for the expected configuration a
*large deviation principle (LDP)* holds with
a good rate function and speed log n.