First passage statistics of modified polya URN processes - Catalig, Migel Antonio P. (National Institute of Physics, College of Science, University of the Philippines Diliman, 2012)
We study the basic Polya urn process and the logarithmic Polya urn process. In the basic Polya urn process, we established the existence of a critical threshol ratio with the highest exit probability. We also considered the case of the interaction of the urn in an outside environment. Based on the capacity of the urn, there exists a critical value for the number of balls in the urn that maximizes average energy.