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The Bernoulli- Laplace model, is a simple discrete model for the diffusion of tw

ID: 2954001 • Letter: T

Question

The Bernoulli- Laplace model, is a simple discrete model for the diffusion of two incompressible gases(fluids) between two containers. It can be formulated as a simple ball and urn model. Thus, suppose that we have two urns, labeled 1 and 2. Each contains N balls, Urn 1 contains j red balls and N-j blue balls and urn 2 contains k red and N-k blue balls. At each discrete time, independently of the past, a ball is selected at random from each urn and then the two balls are switched. The balls of different colors correspond to molecules of different types, and the urns are the containers.The incompressible property is reflected in the fact that the number of balls in each urn remains constant over time. For N = 2 , j = k = 1 find the limit distribution in both containers.

Explanation / Answer

http://www.math.uah.edu/stat/markov/BernoulliLaplace.html

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