Cécile Mailler (University of Bath)
A two-table theorem for a disordered version of the Chinese restaurant process (CRP)
Abstract:
In this joint work with Jakob Björnberg, Peter Mörters and Daniel Ueltschi, we
introduce a disordered version of the CRP in which tables have different weights
(or fitnesses). When a new customer enters the restaurant, they choose to open a
new table with probability proportional to a parameter θ, or they sit at
an occupied table with probability proportional to the weight of this table
times the number of customers already sitting at this table. We show that, in
this model, in probability, a proportion converging to one of all customers sit
at the largest table. We also show that this is not true almost surely, but
prove instead that, almost surely, a proportion converging to one of all
customers sit at one of the two largest tables.