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A two-table theorem for a disordered version of the Chinese restaurant process (CRP).
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 $\theta$, 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 (this largest table changes over time). 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.
Date:
25 November 2024, 14:00
Venue:
24-29 St Giles', 24-29 St Giles' OX1 3LB
Venue Details:
Department of Statistics, Small Lecture Theatre
Speaker:
Cécile Mailler (University of Bath)
Organising department:
Department of Statistics
Part of:
Probability seminar
Booking required?:
Not required
Audience:
Public
Editors:
James Martin,
Julien Berestycki
