# Publications and Preprints

P\'olya Urn Schemes with Infinitely Many Colors
by
In this work we introduce a new urn model with infinite but countably many colors indexed by an appropriate infinite set. We mainly focus on $d$-dimensional integer lattice and replacement matrix associated with bounded increment random walks on it. We prove central and local limit theorems for the expected configuration of the urn and show that irrespective of the null recurrent or transient behavior of the underlying random walk, the urn models have universal scaling and centering giving appropriate normal distribution at the limit. The work also provides similar results for urn models corresponding to other infinite lattices.