Definition
Although whimsical, one fancifully imagines a Chinese restaurant with an infinite number of circular tables, each with infinite capacity. Customer 1 is seated at an unoccupied table with probability 1. At time n + 1, a new customer chooses uniformly at random to sit at one of the following n + 1 places: directly to the left of one of the n customers already sitting at an occupied table, or at a new, unoccupied circular table. Each table thus corresponds to a block of a random partition. (For an account of the custom in actual Chinese restaurants, see table sharing). The probability assigned to any particular partition (ignoring the order in which customers sit around any particular table) is
where b is a block in the partition B and |b| is the size (i.e. number of elements) of b. David J. Aldous attributes the analogy to Pitman and Dubins in his 1983 book.
Read more about this topic: Chinese Restaurant Process
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