Publications and Preprints
P\'olya Urn Schemes with Infinitely Many Colors
Antar Bandyopadhyay and Debleena Thacker
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.
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