Summary: Proceedings of the International Congress of Mathematicians
Hyderabad, India, 2010
Exchangeability and Continuum Limits
of Discrete Random Structures
David J. Aldous
Exchangeable representations of complex random structures are useful in several
ways, in particular providing a moderately general way to derive continuum
limits of discrete random structures. I shall describe an old example (continuum
random trees) and a more recent example (dense graph limits). Thinking this
way about road routes suggests challenging new problems in the plane.
Mathematics Subject Classification (2000). Primary 60G09; Secondary 60C05.
This write-up follows the style of the ICM talk, presented as 5 episodes in the
development of a topic over the last 80 years.
· Exchangeability and de Finetti's theorem (1930s - 50s)
· Structure theory for partially exchangeable arrays (1980s)
· A general program for continuum limits of discrete random structures,
illustrated by trees (1990s)
· 3 recent "pure math" developments (2000s)
· Road routes from this viewpoint (2010s)