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Mean and variance of balanced Pólya urns

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Abstract It is well-known that in a small Pólya urn, i.e., an urn where the second largest real part of an eigenvalue is at most half the largest eigenvalue, the… Click to show full abstract

Abstract It is well-known that in a small Pólya urn, i.e., an urn where the second largest real part of an eigenvalue is at most half the largest eigenvalue, the distribution of the numbers of balls of different colours in the urn is asymptotically normal under weak additional conditions. We consider the balanced case, and then give asymptotics of the mean and the covariance matrix, showing that after appropriate normalization, the mean and covariance matrix converge to the mean and covariance matrix of the limiting normal distribution.

Keywords: variance balanced; lya urns; mean variance; balanced lya; covariance matrix; mean covariance

Journal Title: Advances in Applied Probability
Year Published: 2020

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