Aarhus University Seal / Aarhus Universitets segl

PhD Defense by Dan Beltoft (2010)

Title: Limit Shapes and Fluctuations of Bounded Random Partitions

2013.11.04 | Christine Dilling

Date Mon 20 Sep
Time 13:15 16:15
Location Aud. D1

Bedømmelsesudvalg / Assessment Committee:
Professor Stanislav Smirnov, Université de Genève, Switzerland
Professor Jørn Børling Olsson, Københavns Universitet
Lektor Jesper Funch Thomsen (formand), Aarhus Universitet

Links til resume og ph.d.-afhandling / Please see abstract and PhD thesis:


Random partitions of integers, bounded both in the number of summands and the size of each summand are considered, subject to the probability measure which assigns a probability proportional to some fixed positive number to the power of the number being partitioned. This corresponds to considering Young diagrams confined to a rectangle. When the rectangle grows, and diagrams are rescaled, the probability measure degenerates to a delta measure on a continuous curve, the limit shape. In the intermediate scaling, the fluctuations around the limit shape turn out to be governed by an Ornstein-Uhlenbeck process. Similar behaviour occurs in the related models bounded only on one side or not at all, which were studied by Vershik and others.

Thesis advisor: Nicolai Reshetikhin and Henning Haahr Andersen

Format available: PDF (1436.3 kb)

Short URL: math.au.dk/publs

PhD defense